I'm not exactly sure how well it would work, but you could try a hand capper to put the caps back on a bottle and then carefully remove them again without crimping them.
https://www.amazon.com/Manual-Bottle-Capper-Brewing-Capper-1/dp/B07TZNP2T3
Just re-read your post. Are you looking to completely flatten the caps out to remove the edge crimps?
Here's how l do it: https://photos.google.com/share/AF1QipNmYbTlJxopR9z_LionlZGPWb1HaiuoPu2tKBKGo4SUvILu_ZJH6hRdVTCI22xzEA/photo/AF1QipPPwOidXE6HZUqWxPRLpOF4zZ0Ub_i9va-Hzsrc?key=bVl1MVZjclUzQ21aLWNJUkxEbWRyQWhZZjRzQ29R ...screws and velcro! Super cheap and efficient. If you want more details, let me know...
Depends on the bend. If it's that seriously deformed like u/HomemadeSodaExpert showed than I'll work similar like he does. If it's just a simple bend, I use a bottle capper like this one, recap it and open it without bending.
X-bet MAGNET ™ - Ceramic Industrial Magnets - 1,8 cm (0.7'') Round Disc - Ferrite Magnets Bulk for Crafts, Science & Hobbies - 100pcs / Box! https://www.amazon.co.uk/dp/B018ITTFDM/ref=cm_sw_r_cp_api_glt_fabc_CZYEA093BA38WAMXH65G?_encoding=UTF8&psc=1
Out of stock at the moment but these are the ones I buy. IIRC they were just under £15 for 100.
I had a collection of 43000 different and 6000 and always used 50 slot flocked jeweler trays. They stack easily and help you organize your collection. If you are a Prime Member, here is a link.. But you can get them much more cheaply at Jeweler Supply stores sucxhb as Gems On Display. https://www.amazon.com/FindingKing-Pendant-Jewelry-Showcase-Display/dp/B002HIFHRO/ref=sr_1_34?dchild=1&keywords=jeweler+flocked+trays&qid=1608454985&sr=8-34
HQY Magnet-Automatic Beer Bottle Opener, No Cap Can Escape (New Verision) https://www.amazon.com/dp/B0114C2XNY/ref=cm_sw_r_cp_api_fabc_ifCSFbXKGS2H9
This is what I’ve used. Not sure if it’s the same brand but I’ve always had good experiences with it.
I bought the display cases on Amazon. https://www.amazon.com/dp/B0757CB6RC/ref=cm_sw_r_cp_awdb_t1_fhydEbQMXY9WM
The caps sit snugly in the cases, held gently between the glass and the white foam insert.
Another person asked about the flag caps, so check out my response to them!
Yo Joe, I've actually got a solution for this that is relatively cheap: Film negative sheets . I use this method to store my surplus storage of caps. I just simply staple one end closed and then line them up... it is a pain to get them out though.