Replying to Minor Delamination Repair

So I recently noticed a ~4 inch section of my ski that is delaminating underfoot. The gap between the base and sidewall is barely noticeable, probably less than a millimeter. I have some epoxy and clamps ready to go for the repair, but I don't think I'll be able to get much of the epoxy in deep enough due to the tiny opening. Anyone got any tricks? All I can think of right now is heating up the epoxy and ski and attempting to drip it in, maybe use a toothpick to apply?