Did they ever make funky beatknik jazz in the 60's
 

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you'll probably really like Charles Mingus. there are actually a few of his tracks that either ended up in or heavily inspired some of those old Spiderman soundtracks. i'd say start with Mingus Ah Um

An obvious mention which I'm gonna make anyways is Henry Mancini, but of course he did compose soundtracks so I'm not sure if you think he's relevant. I think he's most known for Breakfast at Tiffany's, but I guess the soundtracks for Peter Gunn or Pink Panther might be more like what you're looking for.

I'm not well versed with this stuff (not sure whether such a movement existed), but 'I'm late, I'm late' by Stan Getz is a wonderful track, which you might like!

That's a pretty near perfect recommendation, Tore. Mancini kinda' rode the border between swing and acid jazz and most of his work is oriented toward television and movie scores.

The Jazz guitarists Wes Montgomery and Grant Green were the primary purveyor of The original acid jazz the likes of what you're seeking. The term is actually used to describe a few different genres not all of which are even jazz. There were so few notable acid jazz artist, primarily because the sound was so west coast influenced. It was a very short-lived sub-genre of jazz, with most of it being produced for television and movies.

You'd probably do well to explore Bossa Nova as a genre. A lot of the same elements of swing and acid jazz can be found in roots bossa nova. A lot of those 50's -70's soundtracks drew heavily from that genre. Of course it does have a distinct latin flavor too it, but I'd Definitely recommend some Antonio Carlos Jobim to anyone. Mr. Dave's suggestion of Charles Mingus was pretty on point too if you want to hear a heavier leaning toward the swing end of things.

speaking of Bossa Nova i'd combine two of the names already dropped here.

Antonio Carlos Jobim is the man when it comes to the style, and the albums he recorded with Stan Getz are freaking awesome. (Jazz Samba and The Jazz Samba Encore!). personally i prefer the Encore!, the first album features Charlie Byrd on guitar and gets too noodle-y for the style. the Encore is nice and subdued, Luiz Bonfa plays guitar on that one being Brazilian as well and it just works a little better for me, the album comes across as darker but i love it. one of my all time favourites.

speaking of Mingus, i think its safe to say his track Boogie Stop Shuffle was a likely inspiration to some of those old Spiderman soundtrack pieces.

Yeah, the similarities are pretty uncanny:

There was definitely some Funky Beatnik Jazz in the 60s and 70s its hard to find here in NZ but its out there! Love it!