I can't find the post, but it was posted some time back on this forum that magazines for the 457 will fit the 4516-1. Others more knowledgeable can provide more specific information.
One caveat on the 4516, 4516-1, 4516-2, & 457 mags - I believe it also applies to the 4506, 4506-x mags / followers.
The original 4516 no dash pistols date to 1988-89 and had magazines with Orange followers as I recall.
As a result of customer complaints (feeding?) for the original 4516 pistols, there were a number of design changes which became the 4516-1 (1989-92) including subtle changes in the metal geometry at the top of the 4516-1 magazines and a change to Yellow followers (1st photo).
There were still some problems observed with the 4516-1 which resulted in the 4516-2 with the dual recoil springs (1993-97). There were also more changes to the top metal lip of the magazines which included the introduction of the Black Follower (2nd photo).
Most of the ones with the Yellow follower were marked "4516-1 only" and/or "Must Have Yellow Follower". I have also seen magazines with the Orange follower marked "4516 only" and/or "Must Have Orange Follower" (3rd photo).
I believe all 4516 and later 7rd variations (457, 4513TSW 7rd, etc.) and all 3rd generation 45 cal pistols after about 1992-93 had the later design magazines with the Black follower. The later 4516 magazines with the Black Follower are supposed to be backwards interchangeable to the 4516 and 4516-1 pistols (4th photo).
Similar Follower Color and upper Metal Lip geometry changes and Follower Color limitation markings have been observed on 4506 8rd mags (5th photo).
Having noted these differences, I will acknowledge that many have found the 7rd mags regardless of original pedigree to function in 4516 variations interchangeably and similarly the 8rd mags in the 4506 variations.
Personally I prefer the later mags with black followers except for range / practice use.
As previously noted the CS45 and 6rd 4513TSW mags have slight differences in metal geometry even though they appear similar and both have black followers. I can not comment on their interchangeability, though many sellers fail to properly identify which 6rd mag they have for sale.