Womanizer and cheater are totally different. A man has to be in a relationship to be a cheater, but he can be a womanizer at any time.
Strange word, that womanizer.
You might think it would mean (a) “to make into a woman.”
Consider sterilize, Americanize, fossilize, crystallize.
(to make something sterile, make something into something American, make into a fossil, a crystal, etc.)
Also (b) “winterize” - to prepare something for winter;
then (c) “hospitalize” - to put into a hospital;
“economize” - I think this is close to sense (a)
“to put one’s house in order.”
“tyrannize” - “to create a tyranny,” rather than “to make a tyrant.”
Strangely enough, “womanize/womanise” dates to 1585-95.