I obey the No1 motorcycle law.
Ride because you want too.....not because you need too.
If you need to keep your battery charged, go out and buy a battery tender for $30.00 or so. Getting on your ride without proper riding gear and riding in challenging conditions, because you NEED to keep your battery charged, is IMHO, asking for trouble.
As for riding in the wet with a KLR, speed is a major factor. The stock Dunlops are a 50/50 tire with solid blocks of rubber that aren't designed to grip wet asphalt. If the blocks had sipes cut into them it would help but they don't. I'm sure there are great wet slab tires for motorcycles, but not for the KLR's.
As for breaking loose when braking, increase your distance, lower your speed and take it very easy with the rear brake. Relax, but be vigilant to the conditions (manhole covers, centerline oil)