Simple Isopropyl alcohol makes a fine, effective and longlasting deodorant. It’s much cheaper than commercial deodorants. In the US, it is sold in two strengths, rougly 70% and roughly 90% — the stronger one works better.
If you don’t like it right out of the bottle, you can get sealed gauze soaked in it, such as a medical practitioner uses to disinfect your skin before giving you an injection. Works great, and it is portable.
Warning: if you shave your armpits, this will sting very badly and cause you to jump up and down and utter profanites.