There are a number of approaches you could try, but you need some info first.
I gave my ultimate magic cards away, so I cant measure the chip resonance capacitor
This will probably be 17pf or 50pf
If you scan your card with TagInfo, it MAY populate that info ( It doesn’t measure it, but it think it is in the manufacturer info )
Is your watch band leather or similar? i.e. does it have a hollow centre or centre that can be hollowed to hold the chip and antenna?
otherwise
How do you plan on attaching it? do you have a plan?
There are some off the shelf antenna options you could grab and experiment with like these
wich are similar to the size and shape you will need for a watch band.
LINK
or
You could do something like this
as you will also find antennas in small circles
Just go to your Chinese wholesaler of choice and type in 13.56MHz antenna.
You’ll want something 15mm or smaller diameter to just drop in and seal up.
Is your watch a smart watch? there may be some issues to consider, but easily mitigated.
Because ideally you want you antenna inductances close, the above antennas may not match.
You could try it and see how you go, or you could try your own by adjusting the wire thickness.
BUT The other route you could take is a little less off the shelf and more maker space.
It’s probably a better option because you know the inductance matches
Disolve the card in Acetone or similar
desolder the antenna from the chip (to make the antenna easier to work with)
Photocopy your watch band and use that as a template to lay the antenna turns ( wound thinner and shorter than the actual strap) lay your antenna out and work out how you are going to attach it ( actually do THAT before winding )
You could do a hybrid
Get yourself the Hornady watch band, pop out the chip from that
Wind your cards antenna around a ~12mm guide
Solder the chip to the ends
Test range
Drop it into the band
Fill with epoxy or cap it off/ plug it up.
If I wasn’t clear, do worry too much about the shape, It is not as important.
You will likely go for a tightly wound Rectangle, Oval or Circle which will all be fine for what you want to achieve.
I would just add, whatever shape you choose, The bigger the better
Hopefully that gets you started on the right track.
Sorry this was rushed and probably disjointed.
Feel free to ask more questions if you need