My question was if I may ask politely for people to switch with me if the reason should clearly be that I do not want to sit near a woman
You can always ask politely. You don't have to specify a reason, though usually one is given as otherwise it is strange.
Things to ensure: (This is the same when you're trying to sit with family or any other reason.)
1) The seat you are asking them to switch to is the same or better than what they are in.
2) Be ready for and accept a no. Even if it seems they have no reason to refuse and are just doing it to be spiteful, they have every right to be, and there might be a reason for that preference that you don't realize. If you absolutely cannot fly sitting next to a woman you need to purchase two seats.