As Selune mentioned, the Watch would not take kindly to an outward display of allegiance to a group that's not the watch. Joining the Watch is akin to formally cutting ties with your family -- your enemies can't find you, you don't inherit any lands, you nullify any former promises of marriage, and so on. If one guy breaks the uniformity of thousands of mice by wearing tokens of his family, this leads to three things
A) His peers, who are mostly lowborn, assume he thinks he's better than them. They beat him in the barracks with in the middle of the night. Aelfric removes his shield and circlet to stay safe.
B) His superiors, who notice his defiance of the rules, penalize him for disrupting the uniformity of the Redwatch. Aelfric is systematically bullied by superiors until he removes his shield and circlet.
C) The superiors of his superiors notice the Watchmice under their watch have allowed one mouse to flaunt his family's crest, which by extension makes them look bad. Aelfric is told to remove the signs of his home, or go back to it.
If you really wanna do a deposed nobleman, I think you should have Aelfric secretly keep tokens of his family around somehow. Maybe a dead sister's locket or a childhood instrument or something. I'm just spitballing here.