If installed in 1976, the adhesive may not be asbestos filled. To my knowledge, the only vinyl asbestos tiles were 9×9″. I believe the asbestos containing adhesive was black.
I would remove everything down to the concrete; you will not be able to remove just one layer.
With all that, I pesonally don’t panic where asbestos is involved; I just make sure I don’t sand it etc so it becomes airborne.
I would use an 8″ razor floor scraper to take up vinyl and adhesive. You should be able to get the concrete clean enough that you can lay the self-stick tiles on it. If you don’t like that idea, there is a sealer that can be applied with a trowel. Or you can remove the adhesive with lacquer thinner.
Self-stick tiles have a reputation of shrinking so that there are gaps between. To minimize that, lay out the tiles dry for a day or so to acclimate to the floor temp and humidity.