Depending on the type of rectifier the power supply uses, if it's a bridge rectifier, you could probably get away with removing the tranny and replacing it with batteries.
It shouldn't hurt it to try.
Alternatively, locate the rectifier and remove it and connect the batteries to the main +- supply line. Make sure you get the polarity right otherwise the amp may smoke and your efforts will be in vain.
One trick to splash proof speakers is the put them in a thin plastic freezer bag and re-mount them. Keep the bag loose around the speaker. The loss of sound quality or volume won't be significant at this level.