I don't need my YubiKey just at work. I need it with me all the time regardless of whether I am even wearing clothes.
The exercise and showers maybe, but feeling like you need your yubikey with you literally 24 hours a day certainly is. I use them extensively and with everything properly set up perhaps need it a couple of times a week at best. Having it on a keychain or in a backpack is fine.
Hate to say "you're doing it wrong" but you (or your company) certainly seem to be doing something wrong to have this level of hassle. No-one would use them if they were this much trouble.