I don't think it would change everything. It's an interesting question though, it deserve some serious meditation, so I took my time.
You intend there's quite a new professional figure, glamorous, stunning sexy women able to pleasure men, maybe with some tech gizmo involved, without any risk and string attached. In fact prostitution always existed, and some men, richer than others, are able to "gift" themselves with an expensive escort to show off and bed later in the night. Such men usually have wives, and childrens waiting home.
It would be more a quantity change, than a quality one. I think youngsters and young men would "use" that new possibility to gain a firsthand experience, every time they want, but soon they will drop it, and start looking for a mate, for a girlfriend and a wife.
Society is centered on monogamy... so there still will be pressure over family. And, if not family, I remember you that we, as men, are quite a competitive and "possessive" kind. We need to belong, and if at now losing virginity is a great "rite of passage", in the world you're describing getting a true girlfriend will be a rite even more important, because everyone would be able to bed one girl, but he will not have a partner, a significant one to live life with... it's not the same going to the cinema with someone that loves you, or paying someone to giggle at your jokes, make some puppy eyes and sexing you at home.
Women would still have their lives, too, so, nothing much would be lost on security.
Yes, they would be delighted, I think. But even then, I think they'll still think in the first stages of their relationships if the man who's holding her hand truly loves her, or the story will eventually fade. Then, they will be as happy a contemporary woman is happy of living in a good relationship. And I think that "Beloved, you know, you don't have to have sex with others, if you truly love me, I'm the only one you'll need" would become a common phrase.
So, I think things would be much the same as they are now. Men have a great sense of belonging and having. Belong to a family, creating one.