I’m not sure strength is an issue here. It sounds like you may be over-gripping your tools.
First, for WI3, most of your weight will be on your feet. Tools will be used primarily for balance (to hold you into the wall). I would suggest doing some top rope technique sessions at a crag somewhere, hanging on to your tools as lightly as possible (thus the top rope).
Second, don’t squeeze. You need to grip an ice tool to swing it, but not to hang from it.
When hanging from an ice tool, your palm should not be touching the tool. If it does, then you’ll be fighting against biomechanics. Biomechanics always wins. In contrast, your fingers should be curled but your palm open and relaxed. There should be a straight line through your joints from your second knuckle down to your shoulder, just the same as if hanging off of a hangboard.