Omega will polish the watch case (a no-no on vintage, pls leave the finish as original), and even if you trust them to oblige the request to not polish the case they will very likely replace "worn" parts like hands, bezel, dial, and crown with new service parts. Omega would destroy the collector's value of the watch's vintage patina that could be worth more than your car (the watch with orange hand).
Never polish things like a vintage watch, gun, or coins (nor replace the cosmetic parts with valuable patina for new parts if avoidable). Many people would be okay using some polywatch creme to remove scratches from the crystal, but if it was going to be sold then it's always best to leave things like that to the buyer, and don't clean it up for them in advance - the buyer may not want the mismatch of a vintage looking watch with a sparkling clean crystal that stands out.
Until you know for sure what you want to do with it, I would not wind it or use it if has been over 5-7 years since it was last serviced, because you may wear down difficult to replace parts which could increase the cost of a service. Any service should be limited to taking the movement apart to clean, oil, and adjust, with new gaskets and mainspring. The original crown and pushers may not be watertight anymore, but a buyer paying what an "Ultraman" is worth would value originality over water resistance, and they can always replace those parts later.
If you MUST, only replace the pushers and crown with appropriate water resistant vintage parts from the same year vintage Speedmaster, not a new service part - some collectors will count the number of ridges and width of the crown, etc to determine that it's not the right part. And even one from a vintage watch that was made a few years away from yours could be the wrong part.
If you get an Extract of the Archives from Omega and it shows that it's really an "Ultraman" then it's quite rare, and possibly worth $20-50K in auction, depending on originality and condition. If it's just a modified Speedmaster (such as the orange sweep second hand) it could still be worth over $10K, especially with the excellent condition "DON" dot over 90 bezel which adds $1500-$4000 to the value of a 1960's watch (condition condition condition).
If I owned one of the watches and it was an "Ultraman" (on the left) owned by my father, I would keep it forever, and I would do the above but only wear it on special occasions (meeting or party) and around the house. For just a regular vintage Speedmaster I would also service, but would more likely wear it on a daily basis, as a reminder of my father.
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