When I conquer Sigil of the Storm with Ivern Legend, can I replace it with a Brush when I conquer and don't need to recycle?

No, you cannot skip the recycle.

You can choose to replace Sigil of the Storm with a Brush token — Green Father's ability says "you may exhaust me," so it's optional. But that does not cancel Sigil's trigger. Here's why:

Both triggers fire simultaneously when you conquer. Sigil says "you must recycle one of your runes" and Green Father says "you may... replace." They both go on the Chain. Even if Green Father's replacement resolves first and turns the battlefield into a Brush token, Sigil's trigger is already on the Chain — triggered abilities are independent of their source once placed on the Chain (FAQ #10867 applies the same principle to Targon's Peak + Ivern). So Sigil's trigger still resolves and forces you to recycle a rune.

The only way out: if you have no runes to recycle, the trigger resolves doing nothing and you still conquer (FAQ #6863). But as long as you have runes, you must recycle one — swapping to Brush doesn't let you dodge that cost.