(This has been initially assigned a Major priority because no workaround exists.)

As noted in the developer forum (link below), there is no way to disable the "Assign Issue" from within the Operations Menu without removing it from all screens in the project.

The problem we are trying to solve is that we have some workflow steps associated with some customized transition screens. In one case, we have an Assign transition that is associated with a screen that does much more than change the Assignee field. We have told the developers on the project to not use the "Assign Issue" link that appears under the "Operations" menu but they still inadvertently use it from time to time.

The desired solution is to remove the "Assign Issue" link from the Operations menu.

We tried to modify the Permissions Scheme such that no one has the "Assign Issue" permission and that does remove it from the Operations screen, but that also removes the "Assignee" field from all other screens and transition screens (including the screen associated with our custom workflow step).

With that said, I think it is just to say that we have found a bug (or an improvement however you look at it). The overrides provided in the Operations menu are useful at times, so removing them is not desired. However, the Permissions Scheme needs to be extended to specify who has permission to actions that are listed within the Operations menu.

http://forums.atlassian.com/thread.jspa?messageID=257298408