Is there a name for these "bait-and-switch" sort of songs?

Johnny Horton, “Battle of New Orleans”

Old Hickory said we could take 'em by surprise
If we didn’t fire our muskets 'til we looked 'em in the eye
We held our fire 'til we see’d their faces well.
Then we opened up with squirrel guns and really gave 'em

Well we fired our guns and the British kept a’comin.
There wasn’t nigh as many as there was a while ago.
We fired once more and they began to runnin’
On down the Mississippi to the Gulf of Mexico.

The reminds me, there is a song I used to hear on a classic rock station, but I can’t remember much of the lyrics, or singer, in the vein.

All I can remember is “I appreciate her but,…”

Familiar to anyone

No, but it reminds me of “Big Bottom”:
[Spinal Tap]How can I leave this behind?[/Spinal Tap]

Strut, Bob Seger.

AHh thank you sir, I have been wondering for a while.

From my far-distant elementary school daze in the '50s (and how in hell has this stayed in my brain after more than 50 years?):

Frankie and Johnny were digging in a ditch,
Frankie called Johhny a dirty son-of-a-

Beaver, beaver, sitting on a rock,
Along came a bumble bee and stung him on his

Cocktail, ginger ale, five cents a glass,
If you don’t like it shove it up your

Ask my no questions and I will tell no lies,
Frankie hit Johnny and now he’s paralyzed.

mentioned “Miss Susie” in the OP, which is the same song.

Oedipus and Jocasta would pucker
And out of her clothes he would shuck 'er
'Till he got a surprise
And he gouged out his eyes
The pitiful, sad, Freudian archetype!

f’ing brilliant. Where did this come from?

“The Freckle Song” by Larry Vincent (from a Dr. Demento collection of '40s novelty songs):

She’s got freckles on her, but she is nice
And when she’s in my arms it’s Paradise
When she gets drunk she gets plastered
She gets drunker than my brother
She’s got freckles on her, but she is nice

Similarly, there’s a protest chant here in Quebec (actually, a line that can be appended to most any protest chant) that goes Aucu-, aucu-, aucu-ne hésitation (no hesitation, where aucu- sounds like au cul, ‘in the ass’)

Not long ago, there was a song on the country-western charts called “Hillbillies”. I don’t remember the name of the group that sang it.

One verse ended with the line, “Hillbillies like to do it in the hay.” Slightly risque, but nothing the censors could cut.

Although, given the song’s rhyme scheme, you were expecting to hear something that would rhyme with “grass”.

There’s also a Dead Milkmen song called Serrated Edge that goes

“My baby sure drives a truck
My baby has a pet duck
My baby sure is good luck
And My baby is one heck of a fffffriend”

Lest we forget - My Ding a Ling.

Not seeing the bait and switch in that one. What’s the obvious other rhyme that’s set up in the lyrics?

And come on people, there’s gotta be a name for this genre!

Have you heard that Mimsie Starr
Just got pinched in the Astor Bar?
Well, did you evah? What a swell party this is.

Why?

Things like this aren’t given a name until someone notes and categorizes them.

On the bright side, nothing’s stopping you from coining a term for it.