Will skipping nonce enchance mining performance given there's more resourceful miner
The blocks you try to mine will have your block reward address in them. The blocks other people try to mine will have their reward address in them. Because the blocks are different, any correct nonces will also be different.

When you mine, you are not competing with other miners in the same search space. Whoever finds their own nonce first wins, but everybody is looking for a different nonce.