Well lover88, long time coming back, but the screws will be more effective and safer, if to my eyes the additional metalwork detailing makes them look a little agricultural, I have seen similar style, are they upholstery pins?
I think I may have taken the opportunity to re-shape the toes, but of course, there is additional skill and attendant risk involved in doing that, and while screwing a nice pair of shoes is one thing, f_cking them up is entirely another !
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Looking back, still think having both straps in black would look good against flesh colored stockings or barefoot, of course, looking now at black shapeless socks, are you covering some hideous deformity, some tattooed message which you do not want the world to see perhaps, is it your partner in them with something like these shoes / feet are made for f__cking?

naughty but nice, while the nude? Strap choice is also OK.
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I might consider adding screw cups to the screws holding the straps particularly as they appear to be countersunk. Screw cups are designed for countersunk screws and in this application, would be used to perform a similar function to a washer, including adding grip and spreading the load on the material among other, while the type of screw, its thickness, the length of insertion into the shoe, its proportion to the material thickness and the way you made the hole through the material, are all relevant to performance under load.
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Not to bore, but such detail is always a consideration. Serious failings in the marine and aircraft industries where boats have sunk and aircraft have crashed due to holes; not only those created by enemy ordnance - shells and torpedo’s etc, and in this instance, less historical, more hysterical, but if a strap gives way, you could fall and break an arm, leg, twist an ankle, bang your head or even sustain an irreparable compound fracture to a nail, the list can get very bloody and just goes on, so best avoid I think, although of course with high heels, accidents do inevitably sometimes happen.
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Back to fun, love playing with and discussing shoes in all sorts of ways.
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As the soles are made of wood, you may find there is a suitable wood filler which chosen carefully, could match to a practically perfect finish, so you could remove the unnecessary old rivets by carefully levering, by drilling or using something like a screw extractor, or a tap from a tap and die set (neither designed for purpose to extract soft rivets and I have not tried) to screw a little way inside the centre of the rivet if it is clear, and slowly pull the rivet out, again some hand skill, planning to avoid damage, and tooling required, then fill the holes. If you cannot get a perfect finish, upholstery pins in their place would cover and match the current style.
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Personally, I might remove all extra metalwork, fill all the holes, and just leave the straps fitted by screws, closer to their sexy original design.
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Slipping your feet into them, feeling the weight distribution change more to the balls of your feet, enjoying that slight instability as you walk, and standing in them, enjoying every extra, delicious, slightly unsteady inch above the ground, crossing one foot over the other, bending forward and feeling muscles stretch and tendons tighten, that model pose which accentuates the feeling of being heeled, looking sexy, feeling feminine, with all that sensory input already, looking down, you see mainly the straps crossing sexily over, cradling your foot, does anything else matter quite so much.
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w.voyeurweb.com/hall-of-fame/view/53090-whalenet-stockings
download/file.php?id=477927&mode=view
Not exactly right, but some idea, although caution, you may not look that good.....
Thanks to original posters
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I must take a picture sometime, as I have something in some ways similar except, thinner sole, different wood, with original adjustable buckled straps, which were the reason I bought as they were most likely to fit, OK practically not similar at all, but your heels also different, as mine are wooden, although both will likely have some additional internal structural support inside.
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As well as feeling so sexy to walk in, do yours “ping” ? Mine make a resonant “ping” with each step, particularly noticeable on hard tile floor, sure I have heard others do the same out sometime, and somehow makes them even sexier to me, for reasons which are anyones guess, just like the whole shoefetish perhaps, but even just the thought of that noise is erotic and arousing to me now.
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The majority of my repairs and modifications recently, have been re-attaching soles / straps - thixotropic adhesive, not gorilla glue, although not tried clear, - but mostly making additional holes in straps so my latest strappy beauties fit. You may consider a simple task, but I have mentioned problems with holes at length, and I have found and would seriously recommend to buy quality and correct size hole punch / cutter, those I had used from hardware shops previously are wrong size and do not do the job cleanly, and in addition, always first consider and then mark the position carefully, then one final check before that click! - of joy when they fit, and some disappointment if 4mm out......
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Of course, my outstanding project was for modifications which would produce a vibrating shoe that would cause anyone wearing to have the most incredible intense and uncontrollable desires, that would in turn of course, transfer into the most amazing shoesex and any other fun I desired, but could be in some ways considered an abject, miserable failure.
I maintain that, and as I fully described and posted on the board, it was a great idea, they were ideally selected, then both electrically and mechanically engineered to perfection, it was solely a failing of female biological engineering which at the final turn, let me down, although, on the way....

Ah well, back to the drawing board, - err CAD CAM
CUM program.
Sorry long addition, hope some fun, even some use.
Good luck.