I expect dishonorable discharge for refusing will soon be the only way out for them.

Refusal to move to a new duty station (while continuing to serve at your current one) typically results in no more than a "may not re-enlist after end of service" code on one's discharge papers, and anyone who has re-enlisted must refuse their final move (fun little trick, that).

I'd actually expect anyone who declines the jab to get the same discharge status they would otherwise have gotten - at worst, general under honorable conditions, which can be upgraded to honorable through administrative action after service.

Furthermore, if an other-than-honorable discharge is the result of not getting stuck, commanding officers are going to start outright defying the vaccination orders in some parts of the military where commanders are generally more based.