Another option is to have the levels as branches and the player can move around them by selecting a "parallel branch".

So after level 3 player can chose left or right route ( 2 levels each way) before they rejoin at level 6

You could make certain style levels as the left branch, other style a right branch (thinking vs reflex? I don't know what your game is)

That way the player has a chance to navigate past disliked levels.

I don't think wanting to skip a level is necessarily a sign that the game is bad, especially for a puzzle game. Sometimes a player just gets stuck on one puzzle, and skipping that one puzzle is better than giving up on the game entirely. If every player wants to skip the same level, then that level is probably bad, and if everybody wants to skip as many levels as possible, then the game itself is probably bad, but if a minority of players all skip different levels and most players don't skip any, then the game is probably fine.

I think the best way to approach level skipping is to always give the player a choice of multiple levels to play, with no penalty. For example, you could start with levels 1 through 5 unlocked, and unlock one additional level for each level completed, so that there are always five unlocked uncompleted levels available to pick from. If the player is permanently stuck on one level, they can just skip it completely, but the player also has the option of skipping a level for now and coming back to it later.