Well, there's two ways to take some of that edge off.

[He tosses a Pokéball up and down as he speaks. Why? Just for the heck of it, really.]

The quickest way's to just fly over the cave, but if you're dead set on passing through...

[He snaps up the ball in his fist and sets it down on his nightstand.]

I recommend packing a fire type with you. Melting through some that ice makes the path a million times easier.