Answer:
Warily
Step-by-step explanation:
A very cautious mouse would warily walk past a sleeping cat. When someone is wary, they are cautious, careful.
To maneuver means to move skilfully or carefully, but it would not be used in the context of a mouse. For example, you could maneuver while driving a car.
The remaining two words have completely different meanings. Matronly means of, relating to, or having the characteristics of a matron (usually a mature and dignified married woman who has an established social position).
Odious means extremely unpleasant.