Good sealant for a wet surface?

Nothing is going to adhere well as long as the pipe is wet. The correct way to fix this is to re-solder the joint, but you might get away with some JB Weld for a short time. Goop and flexible sealants won't hold under pressure. Even though there are only a few drops escaping, the pressure may still be too much for a sealant. JB Weld is stronger.

Turn off the water supply farther back, then drain the lines by disconnecting the hose to your washer. Let it drain into a bucket. Alternately, you could let your washer try to fill until water stops coming out. Either way, you have to get the water and pressure out of the line. Dry off the leaky solder joint and glob JB Weld over it.

Frankly, once you've drained the lines, you're only a few steps away from fixing it the right way by re-sweating the solder joint. If your soldering skills aren't up to it, you might want to check out solderless fittings. JB Weld will work as a temporary fix.

All the above are good suggestions but here is one more:

Go to any marine shop and buy yourself some underwater glue - it is used to seal underwater leaks on boats.

Get a tube of lexel its a clear tube with red tip it will help temporarily

Have it resoldered. Jo Ann