I keep one in my wallet, for geocaches and I don’t touch the customer pen at the store to sign the receipt https://www.amazon.com/NarwhalCo-Pocket-Wallet-Planner-Passport/dp/B0776LK634/ref=mp_s_a_1_4?crid=23FCKEF06GF2R&keywords=narwhal+mini+pens&qid=1654427274&sprefix=norwal+mini+pens%2Caps%2C90&sr=8-4
That’s why I keep one of these in my Wallet so I always have a pen on me. https://www.amazon.com/NarwhalCo-Pocket-Wallet-Planner-Passport/dp/B0776LK634/ref=mp_s_a_1_3?crid=38FDENAUPLI4G&keywords=narwhal+pen&qid=1653441476&sprefix=narwal+pen%2Caps%2C93&sr=8-3
How dexterous are you? Technically you can operate a fisher bullet pen with one hand, although it isn't practical if you're using the pen one handed very frequently.
I found these on amazon, they might be similar to what you're looking for.
Not sure if I’m allowed to post links but these pens have been great for me, they write really well and they’re short enough to clip into the wallet
NarwhalCo Set of 2 Small Pens... https://www.amazon.com/dp/B0776LK634?ref=ppx_pop_mob_ap_share
Be careful with the clip. It's broken off of two of mine.
Edit: these have a much sturdier clip.