To make the work easier on you, I would start with the AoR careers as is then start replacing names and skills when needed. AoR since Mouse Guard seems more militaristic then fringe.
For example, careers could be Commander, Diplomat, Craftsman (from Engineer), Guardsman (from Soldier), and Scout (from Spy). If you need a naval career (never read Mouse Guard) then convert Ace to Sailor. Or Ace to Beast Rider?
An example of a specialty might be Soldier-Sharpshooter becoming Guardsman-Archer. Glancing at the Talents and Skills, you may not need to rename or redefine much. Talents might work as is. Ranged (light) could include spears, slings, rocks, thrown knives while Ranged (heavy) becomes longbows, crossbows, shortbows. Possibly divide Melee into Melee (light) and Melee (heavy) since it's a middle ages setting with a military slant.
Completely designing Mouse Guard from the ground up to use FFG's narrative dice would be a huge endeavor. Reskinning AoR might be much easier for you.
Edited by Sturn
With a suitably terrifying pet Stoat?