In some hands, the ICM is not going to estimate your equity accurately (and then ICM Explorer will not help much directly). The ICM doesn't see position relative to the blinds, but that position is important here, and it means that if you fold, you will be in much worse shape than the ICM estimates. That means you are not as risk-averse as ICM Explorer says. ICM Explorer assumes that if you fold and outchip the short stack 350:90, you are a big favorite to make the top two instead of closer to even since you would post the small blind all-in.
If you fold and then win in the small blind, the short stack could still survive two showdowns while you post the big blind all-in. It's not easy to see through that, but winning next hand might still let you bust out 15% of the time. Folding and then winning gives you a little chance to place first, but let's say 6%, for about 6%-79%-15% in case you win, or about 3%-40%-57% from folding, total 24.9% of the prize pool.
If you call and win, you aren't guaranteed to make the top two, but you have better chances, although you may have to sacrifice some chances to win. I would eyeball it as that calling and winning is worth about 27%-66-7%. With 30% wins, that makes calling worth 8%-20%-72%, total 24.4% of the prize pool. So, from this calculation, the decision looks like a close fold.
Also, with a 4k stack if you win now, you will have FE for HU. which is another huge future game aspect to consider.
I would call that negligible rather than huge. The extra chips give you a greater chance to win, which is important, but how you might get to play is unimportant. Once you get heads-up, unless you have a read that you have a large skill advantage in that phase of the game, you should assume that your chance to win is in proportion with your stack. If you start with 25% of the chips, you should assume that you win about 25% of the time.