Slow Rollin’ Mama from the Dick Tracy soundtrack. Sung by LaVerne Baker.
A Guy What Takes His Time by Mae West.
You could give a nod to Lucille Bogan and sing Shave 'em Dry.
OMG! Just watched this, and it is everything you could possibly want! This one gets me vote! 
Squee! Right back at you! This totally needs a revival.
“I Never Do Anything Twice”, a song by Sondheim, from the movie “The Seven Per Cent Solution.” Sultry, very risqué, and very funny. Hereis, I think, the original by Millicent Martin (anyway, my favorite version).
“peel me a grape” I think fits your description, it is sultry but the lyrics are clever (in my opinion) Amazon.com
Any song can be played and/or sung in any key so as to match a vocal range. Unless you’re somehow stuck with an accompaniment in the wrong key, range is not an issue. It’s not the song itself but the particular rendition of it that determines this.
Wrong link?
I recommend a perusal of the Cole Porter Songbook. Nobody did naughty yet classy pop songs better.
“Let’s Do It” SAYS it means “let’s fall in love.” But it is clearly about doin’ it. Here’s Rudy Vallee’s 1930 version – he was a tenor and a crooner – but lots of women sing it, too.
“Too Darn Hot” is a lament about how we don’t like to screw when it’s hot outside, from the days before universal air-conditioning. Here’s Ann Miller’s version.
Ella Fitzgerald’s is also on YouTube, and is better, but she didn’t have Ann’s legs.
Making’ Whoopee!
Blues In The Night
Also, this
It’s true you can move the vocal range around. But the actual range itself, i.e. between the highest and lowest note, matters, too.
For example, the range of the Star Spangled Banner is one and a half octaves. While most people can achieve that with practice, a totally untrained singer can have trouble with a range that wide. The general rule for songs you want anyone to be able to sing is to stay close to an octave.
Also, just because it’s in your actual range doesn’t mean it’s in the usable part of your rang, let along the part that sounds the best.
That said, the original All About that Bass has a range of an octave and a sixth, which means the OP has a pretty healthy range to work with. Especially if she sounded anywhere even remotely close to as good as the singers in that video. I’m pretty sure they switched singers at least once because one of women couldn’t sing high enough.
Quite right, and something to consider with any song. To avoid confusion, let’s call the latter concept, difference between lowest and highest note, the span, and use range for soprano/alto/tenor/bass and such.
The OP seemed to think that the range for a song is fixed, and I wanted to make sure she knew it’s not.
The span, as you say, is fixed, and may or may not be an issue.
Miss Otis Regrets?
Ruth Etting - Button Up Your Overcoat (1929)- Works well as a funny strip song if you start with an overcoat -
Unfortunately, my accompaniment is probably going to be limited to whatever I can find as a downloadable karaoke version, so that is why I was originally looking for something lower to start with. If it’s a simple piano part, I might be able to do it myself and transpose as necessary, but my ability to play anything beyond basic chords has atrophied over the years.
But I see I have a lot of links to check out when I’m at a computer with speakers. Thanks, everybody!
Ukelele Ike, I had thought about “Let’s Do It,” but I wasn’t 100% sold on the idea. I did not consider “Too Darn Hot,” but that’s definitely a possibility. I had also been toying with “Let’s Misbehave,” which might be my favorite Porter song … my problem was that I got stuck on the idea of what I did last time and couldn’t expand my brain to think of other ideas without help. 
If you’re comfortable singing from a different sexual orientation maybe you could do a torchy treatment of Leonard Cohen’s One of us cannot be wrong
I lit a thin green candle, to make you jealous of me.
But the room just filled up with mosquitos,
they heard that my body was free.
I don’t know if a karaoke version can be found, but I rather like ‘Big long Slidin Thing.’
https://www.youtube.com/watch?v=aaFfJSC6uz8
Dinah Washington recorded it in '54.
Since it’s the holiday season, the one that immediately come to mind is Alison Brie on Community singing Santa Baby. Perhaps not quite a torch song, but it’s funny and almost sexy.