We are talking about this song, right?

The meaning has only shifted for the verb. The noun still has the original meaning of “a kiss”.

So it’s all fine 😀

Trusting to this reference, we see that in this song the word “baiser” is the noun and so it is unmistakeably recognised as such in the song. This word, “baiser”, is also a verb and it can be a coarse term only when it is used as a verb; therefore there is not a chance to induce in anyone’s mind the slightest hint of the coarse meaning. Someone indulging in such plays on words would not only be deemed to have a naughty mind but as well to be silly. Let’s not forget that in French there is no other equivalent for the noun “kiss” than “baiser” when you are talking of kisses on the mouth: the word “bise” and much more so the diminutive “bisou” are improper for that and can be used only for kisses on the cheeks; for kisses on other parts of the body you have to use the noun “baiser”, which can also be used when the kiss is on the cheeks. Note that “baiser” is a rather dignified term, much more so than the former two nouns.

• Il lui donna un long baiser sur la bouche à en perdre haleine.
• Après un baiser à sa mère elle se retira.

The problem you are raising can only occur when the verb is used and then again only in the company of persons of low morals. In fact you’ll find the verb in the whole of the serious literature of the French language and it means strictly “to give a kiss“; you should never fear to use it as seems proper in that context as long as you keep to the company of person who are concerned with literature.

• Elle baisa la main de sa bienfaitrice et la remercia. (such sentences are to be found in the older literature.)