This is not something . . . . . . . . we like to do.

'which' is a determiner pronoun asking for information specifying one or more people or things from a definite set. It is the suitable word to use in the sentence.
'Who' is a subject pronoun that is used to describe who performed an action or who is in a specific state. 'Whom' is an object pronoun that refers to the person who was the recipient of an action. 'Whose' is a possessive pronoun that refers to the person to whom something belongs.