For Mutated Mouser and Switcheroo, can I activate Switcheroo from hidden before Shield activates on Mutated Mouser?

No, you cannot "activate" Switcheroo before Shield activates because Shield is not a triggered ability—it is a passive effect that applies continuously as long as the unit has the "Defender" designation during combat.

Why this interaction happens:

1. Shield is Passive: According to Rule 814.1, Shield is a passive ability keyword. It does not go on the chain and cannot be "responded to." It automatically applies its Might bonus to the unit the moment that unit is designated as a defender in combat.
2. Timing of Switcheroo: You can play Switcheroo from Hidden (which grants it [Reaction] timing per Rule 811.6) during a combat showdown. However, because Shield is passive, the bonus is already active and included in the unit's Might value before you even have a chance to play Switcheroo or while it is on the chain.
3. Snapshotting: Per RiftJudge FAQ #8532, Switcheroo snapshots the current Might of the units when it resolves. If Mutated Mouser is a defender, its Might value already includes the +2 from its Shield keyword. Switcheroo will swap that total Might value, but the Shield bonus itself remains a passive effect attached to Mutated Mouser for the remainder of the combat.

Summary

Because Shield is not a trigger, there is no moment where Mutated Mouser exists as a defender without the Shield bonus being applied. Any Switcheroo you play will be calculating the swap based on the Might value that already includes that Shield bonus.