Can we swim forward in space with wide enough arms or wings attached in vacuum?
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Not meaningfully.
Swimming relies on Newton’s third law – for every action, there is an equal and opposite reaction. More specifically: When you swim, your limbs push water. The water pushes back on you, and this push causes you to accelerate.
In the vacuum of space, there is nothing for your limbs to push against. You can flail your arms and legs about however you like, but all you will do is change how you’re rotating. In order to move through a vacuum you need to eject mass away from yourself in the opposite direction that you want to travel. This is what rockets do: They eject mass (exhaust) at high velocity to generate thrust. If you want to move, you would likewise need to eject mass away from yourself.
Technically, there actually is mass in space, but it’s very diffuse and for all practical purposes it may as well not even be there – roughly on the order of one atom per cubic meter. This is nowhere near enough mass to generate meaningful thrust for a massive object like a human.
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