I find I can tell how good a fitter is by how many different size hammers he has in his tool kit.
If it is just one, and that one is a big one, run, don't walk, away.
The size of the hammer has to be carefully matched to the job in hand, and isn't the rough general use tool some might think them to be.
You are correct in the problem of carrying a hammer on a bike, and over the years I have come up with many solutions.
Carry a hatchet.

There is an Australian Army entrenching tool on the other side, very handy for cooking with camp ovens.
I used a tube spanner from my BMW tool kit to provide the handle for a separate hammer head, no photos sorry.
My Hatchet in use "adjusting" the rivets on my Cali 2 rear guard late last year.

A carefully applied rock is always an option, the unfriendly comment that you can fix a Hardly with a half brick and a cold chisel assumes you actually have both on hand.
My rotors don't get stuck
