Yes, you can say that. It doesn't matter which question word you are using. Here are a couple of examples from COCA:
She wanted a guy on whose shoulder she would do the crying.
Today, we are the legatees of all the giants on whose shoulders we stand.
As CGEL seems to suggest (see below), if a preposition isn't a part of a phrasal verb (a fixed combination of a verb and a preposition, such as tell on), it can be either moved to the front of the clause or left at the end. The first phenomenon is called pied-piping; the second, preposition stranding. Both are well explained here and here. Generally, it is more natural to leave the preposition at the end, especially in informal speech.
However, if a preposition is a part of a phrasal verb, whether it can be moved to the front depends on the verb. Here is what The Cambridge Grammar of the English Language says about it (Chapter 4, 6.1.1):
i the city to which I flew [relative]
ii To which city did you fly? [open interrogative]
There are alternants with a stranded preposition (the city which I flew to, etc.).
Fly to isn't a phrasal verb: you can just as well fly through or fly into something.
Consider now the behaviour of specified prepositions in these constructions, the mobile to selected by refer and the fixed across selected by come:
[6] MOBILE PREPOSITION FIXED PREPOSITION
i a. the book to which I referred b. *the letters across which I came
ii a. To which book did you refer? b. *Across which letters did you come?
Across cannot be moved to the left of come, so only the versions with stranded prepositions are admissible: the letters which I came across; Which letters did you come across?.
Both refer to and come across are phrasal verbs. The to in refer to is mobile whereas the across in come across is fixed.
This also applies to cases where a phrasal verb has a direct object (me in the examples below):
[12] MOBILE PREPOSITION FIXED PREPOSITION
i a. He referred me to a specialist. b. He got me through the biology test.
ii a. the specialist to whom he referred me b. *the test through which he got me
iii a. To whom did he refer you? b. *Through which test did he get you?
The [b] examples contain the transitive idiom get through, “help pass”, and here the specified preposition through cannot be moved.