What you can do for this is to have the docker snap plug a content interface like this:
and then have these other credentials snap expose content interface slots like this:
and then the docker snap would also need to add
$SNAP/credentials-helpers to the $PATH for the dockerd daemon.
After installing the second snap alongside the docker snap, you would have to connect the interface with something like:
$ snap install docker
$ snap install docker-credential-secretservice # (or whatever the snap is called)
$ snap connect docker:credentials-helpers docker-credentials-secretservice:credentials-helpers
$ snap restart docker
Note that since this would be using the content interface, the docker snap would only auto-connect to these credential snaps that are published by the same publisher (i.e. Canonical currently), but if auto-connection to another snap is desired, that can be requested through the #store-requests category on this forum.