Unfortunately it is not possible to trigger asset actions from the user page. In order to do what you want, your support engineers will need permissions to view assets and view the actions.
If you don't want them to have access to viewing the assets, then the only options would be to let just let them connect to the asset of the user manually. They can still see the asset name of the asset that was linked to the ticket. I don't know if that helps in any way or not.
Regardless, I'll add your feedback to the corresponding feature request.