Monstrous Physique can be used as a substitute for exotic weapon proficiency and UMD

[ATHATH]

This spell functions as monstrous physique I, except it also allows you to assume the form of a Tiny or Large creature of the monstrous humanoid type. If the form you assume has any of the following abilities, you gain the listed ability: climb 60 feet, fly 60 feet (good maneuverability), swim 60 feet, darkvision 60 feet, low-light vision, scent, freeze, grab, leap attack, mimicry, pounce, sound mimicry, speak with sharks, and trip. If the creature has the undersized weapons special quality, you gain that quality.

Mimicry (Ex)
A doppelganger is proficient in all weapons, armor, and shields. In addition, a doppelganger can use any spell trigger or spell completion item as if the spells were on its spell list. Its caster level is equal to its racial Hit Dice.
I'm, uh, not exactly sure what that last sentence is supposed to mean. Is it supposed to replace the CL of the items it's invoking with the number of racial HD it has? If it has no racial HD, does it use a CL of 0?

Credit to https://rpgwillikers.wordpress.com/2016/10/28/musings-on-the-metamorph/ for being where I found this trick from.

[Treblain]

It would be relevant to staves and other items that can use the user's caster level. Also for scrolls when determining whether the user can activate them without a check, though not changing the caster level of the scroll.

Edit: Missed the issue of the spellcaster taking doppelganger form. There's probably no clear answer, though the best approach that comes to mind is taking the hit dice of the doppelganger (4) as the caster level.

[Firebug]

Are you sure it doesn't mean this monstrous humanoid's ability instead?
Green Hag monstrous humanoid: Mimicry (Ex) A green hag can imitate the sounds of almost any animal found near its lair.
Yay for overloading game terms.

Spell trigger items don't really care what you CL is, so that part doesn't matter. For Staves specifically, you can use your CL if its higher than the Staff's CL. Since you have 0 actual racial HD for that ability, anything the Staff has is going to be higher.

If your CL on spell completion items(ie scrolls) is too low, you have to make a CL check, which is DC 1+ CL of the item and you roll d20 + your CL. In this case, its just a flat d20+0 since you have 0 racial HD.
If you fail, make a wisdom check DC 5 and if that fails you get spell mishap. If you failed the CL check but not the wisdom check, the scroll is not expended.

So essentially, it gives you a chance to activate any spell completion/trigger item. You just might have to try a few times and hope you don't roll a 1 on the wisdom check (dependent on your wisdom of course).

[ATHATH]

Are you sure it doesn't mean this monstrous humanoid's ability instead?
Green Hag monstrous humanoid: Mimicry (Ex) A green hag can imitate the sounds of almost any animal found near its lair.
Yay for overloading game terms.
Both of them are named "Mimicry".

;)