Is the vahana (mount) of Lord Ganesha a shrew or a mouse?
Ganesha in scripture rides on the mouse, the word 'shrew' is never mentioned in that context.
I won't quote every instance of it being mentioned, but here are two:
Śacī said :-- “Indra has got for his vehicles the horse Uccaiśravā, the Airāvata elephant and the chariot; Vāsudeva has got vehicle Garuḍa; Yama has got his buffalo; Śaṅkara his Bull; Brahmā his Swan; Kartika has got his peacock and Ganeśa has got his mouse.
Then Śumbha and Gaṇeśa seated respectively in a chariot and on a mouse fought each other with volleys of arrows.
Gaṇeśa hit Śumbha in his chest with an arrow and felled his charioteer with three arrows on the ground.
Then the infuriated Śumbha covered Gaṇeśa with a shower of arrows. Hitting the mouse with three arrows he roared like thunder.
The mouse pierced by the arrows, shook with acute pain. Gaṇeśa was thrown off (his vehicle) and he became a foot soldier (as it were).
Then Gaṇeśa hit Śumbha in his chest with his axe and felled him to the ground. Thereafter he mounted his mouse again.
atha śuṃbho gaṇeśaśca rathamūṣaka vāhanau | yudhyamānau śaravrātaiḥ parasparamavidhyatām || 13 ||
tato lambodaraśśuṃbhaṃ hatvā paraśunā hṛdi |
apātayattadā bhūmau mūṣakaṃ cāruroha saḥ || 17 ||
As we see, the original Sanskrit version of the Shiva Purana does indeed use the word 'mūṣaka', which, as a Sanskrit dictionary will tell you, means 'mouse.'