Correct 20 or 22 Tooth cog for 1962 Typhoon?

[SantaCruise]

I'd like to swap out my 18 tooth rear cog for something a little bigger to make it a little easier to navigate some hills. I have a single speed, red-striped, Bendix hub. I don't understand the compatibility of the cogs to other years or even other manufacturers. For example, this 22T cog is for a Bendix hub but the description says compatible with 1963-1996.

https://www.ebay.com/itm/VINTAGE-BE...h=item23749c7ed0:g:SbwAAOSwPCVYAU8x:rk:2:pf:0

If this isn't the correct cog for a 1962 Bendix, what should I be looking for?

Thanks in advance for the help!

 

[SantaCruise]

Apologies... I meant to post this in the 'All things Schwinn' forum and have reposted the same message there.