Are you lifting to maintain your strength or to get bigger/stronger?
If you're just trying to maintain your power, then just lift weights for a set after your boxing.
If you're trying to get bigger and stronger, then it gets a little more complicated because you've gotta push yourself and then you'll be sore for a day or two.
If you just wanna use weights for high reps for conditioning, then it doesn't sound like would be any problem at all because after all, they're offerering a class at that time and that's what many pro's do right?
I think it would depend on your schedule though, like if you box mon,wed,fri........you could do the circuit training on tues and thurday (granted you aren't sore) so that when you box you'll have a full amount of energy since that type of work wears you out.
Either way both have there pro's and con's, do whichever one you like. Or try doing both for a week and see which works better.
best of luck