I sometimes use a Roland Mobile Cube for harmonica and it gives me excellent clean sound. I use six rechargeable AA batteries and they give me a good six hours. It's very portable and, volume-wise, punches way above its weight. It has standard jack-plug inputs (you could play a backing track through it to accompany your amplified self!) and a good range of adjustments. The standard advice always applies: try it out in the shop with your intended mic/pickup. If they won't let you try it, walk away.

It's probably worth saying that most sessions wouldn't welcome you with an amp in a month of Sundays. I understand your issue apropos of mandolins (I can NEVER hear the damn things!!), but no session I've ever experienced would have needed an amplified guitar. The decibel levels at your session must be close to danger point!