No. They need to Hit.

I think you're reading too much into wounding. There's no reason I can think of, in terms of defined game terms, to think that wounding refers to damaging vs. hitting. In other words, the rules don't tell us to prefer one over the other. In general.

However, flip back a few pages: "Player Characters as Lycanthropes" says, in part

A humanoid hit by an attack that carries the curse of lycanthropy must succeed [on a save]... or be cursed. (MM. p.207, emphasis mine.)

There it is, as you first described: the save against cursing is part of the "Hit" clause and comes into play whenever a bite hits, even if it hits for no damage.

Some have expressed concern about what hit points represent, and whether a zero-damage hit is an injury or not. That way lies madness, I think, and we don't need to go there as Hit is a defined term.

Lycanthropy can be passed down to children, but isn't mentioned as sexually transmitted

The Monster Manual entry on lycanthropes (p. 206) says:

Curse of Lycanthropy. A humanoid creature can be afflicted with the curse of lycanthropy after being wounded by a lycanthrope, or if one or both of its parents are lycanthropes.

There is no mention of lycanthropy being passed on to sexual partners. In particular, the phrasing "if one or both of its parents are lycanthropes" suggests that sexual contact won't usually transmit the curse of lycanthropy, unless sex always leads to children on the first try - otherwise, both parents would be lycanthropes as a result of having sex, so it wouldn't be just one parent.

The only ways mentioned to pass on the curse of lycanthropy are:

• being wounded by a lycanthrope (most of the statblocks show that it's transmitted by a bite or a similar attack)
• being the child of a lycanthrope

A cursory online search (including the Wikipedia article for lycanthropy in D&D) indicates that these two methods are the only ways of passing on the curse as described in previous editions of D&D as well. (According to the Forgotten Realms wiki entry, the 4th edition Monster Manual has it only as a hereditary condition.)

Anything beyond what's stated in the quoted entry would be up to you as the DM. I don't think it'd cause any mechanical problems to have lycanthropy be sexually transmitted if you wanted it to be, though there might be some narrative consequences (lycanthropes might be reluctant to have sex for fear of passing on the curse - or they might only do so after revealing their true nature to their partner).