I know I'm coming late to the party, but Wikipedia now has several entries that I think are either what you are asking, or adjacent to it. I am assuming that you are talking about something like the "Shaving Cream song" that I sang as a kid.
I first found the descriptive phrase Mind Rhymes in the title of an entry from JSTOR: https://www.jstor.org/stable/25475703. The 1-page preview isn't enough to show a definition, but the use of "Shaving Cream" in the title is what found it for me.
I did a little searching based on the article, and eventually found the article "Subverted rhyme" on Wikipedia, which was a redirection from "Mind rhyme" (no 's'). They also include the phrase teasing rhyme and presumably a redirection may be available from there, too.
Their examples include (from cheerleading):
Raa Raa REE!
Kick 'em in the knee!
Raa Raa RASS!
Kick 'em in the other knee!
There is also a reference to the poetry term enjambment which may be relevant to you.
I have heard three different approaches to this in (non-parody) rap music. The first is simple omission of the word or phrase. I would call this a "mind rhyme" since the expectation is that you will "fill in the blank" mentally. This is a stock approach to editing a song with potentially offensive lyrics into a lower-rated or offense-free content. (Which happens frequently in rap music. Surprise!)
The next is the substitution of a sound, noise, or musical passage (other than the simple "bleep" of censorship). A record-scratch is common. Or sometimes a recording of a related sound. (For example, a gunshot sound to replace "shoot", as in Public Enemy's Burn, Hollywood, burn!) I'm not sure what to call this, other than an elaborate form of censorship. It isn't really "teasing", nor is it "subverting." It can fit under "mind rhymes" but (as in the PE song above) it isn't always used with the rhyme target. It seems like there might be a word, in line with the poetical Oh, noes, mah toes!; Metropolis; & Schenectady (*) that describes this.
Finally, there is the substitution of another word. Like, "can't stop starin' at her ti-ti-ti-ti- face!" This is distinct from the enjambment/shaving cream approach of completely changing lyrical scheme. This is definitely (IMO) a "teasing" rhyme.
(*) Onomatopoeia, metonymy, & synecdoche, if you're nasty.