Which animals can and can't be prefixed with "she-"?

The prefix "she-" isn't listed in the dictionary. The only "she-" animal that is listed in the dictionary is a "she-wolf." There are no other "she-" animals listed.

The OED, while it doesn't list "she-bear" separately, it does list it as one of the two possibilities of "she-," along with "she-wolf," under the definition of "she."

This site has the following list of female terms with "she-":

she-ass (mule), she-bear, she-chuck (woodchuck), she-fox, she-goat, she-lion (lion & cougar).

She-bear is mentioned in English Bibles

Oxford English Dictionary 2d Ed. has a subsense of a dictionary entry "she":

9. Female. Applied to animals, as in she-ass, she-bear, she-wolf (also fig.), etc.; she-dog, chiefly transf. = bitch 2; she-dragon, a female dragon; also transf.; she-lion slang, a punning distortion of ‘shilling’; she-stock, -stuff U.S., female cattle.

OAD 2d Ed. also has she-ape, she-raven, she-sparrow, she-cat, she-dingo, she-panther, she-lion, she-tiger, she-pigs, she-whales, she-fairies, she-devil, she-griffin, she-giant, she-furies, she-cousin, she-pensioners, she-priest, she-bishop, she-waiter, she-surgeon, she-slaves, she-fool in the definitions and/or examples.

Webster's Unabridged 3d Ed. has she-ass as a dictionary entry, and she-goat, she-fox, she-serpent, she-monster, she-demon, she-wolf, she-mule in the definitions.

Besides, Unabridged M-W has she-crab "an immature female blue crab".