Does anyone here train boxing with a hiatal hernia?

I don't mean fighting or sparring, but simply hitting the bags and mitts. I was thinking that hitting the bags and mitts (not at full force) might help me to stay toned since I'm not able to lift weights (I tried lifting small weights but it didn't work out for me as I started getting pain again in my abdomen).

I know that with proper form you engage your core as you throw punches... but what If I just throw punches with no real power behind them? Gosh... I just want to exercise one way or the other... Hiatal Hernias suck sooo much :(