Wh-movement tends to come in two forms in conlangs, as far as I can tell: English-like or wh-in situ. Let's consider some other options! This post was inspired by some questions in the conlang mailing list.
1. Wh-at the end
There are, apparently, some reasons to consider this highly unlikely in languages. OTOH, it might not be entirely unattested.
2. Wh-in wackernagel
The Wackernagel position, i.e. the second word in a clause, seems a rather natural option.
Both the position after and before the verb seem to make sense as possible attractors for the interrogative pronoun.
4. Discontinuous wh
There are further complications we can consider, such as discontinuous-wh. I find this most likely for two types of interrogatives: determiners and adjectival interrogatives ('what type of a', 'yes/no-query determiner', 'which', 'of what qualities', etc).
These actually occur in some Slavic languages with interrogatives like "kakoj" and "kotoryj".
Anyways, discontinuous-wh can probably be combined with any of the three previous forms, and in different ways - maybe the head noun is moved instead and the wh remains? Maybe vice versa. Different movements for both parts of the interrogative noun phrase seems unlikely, but parts of the noun phrase may well be pulled along with the interrogative particle.
Let's imagine "Q" is an interrogative particle that forms a yes/no-question focused on the noun it belongs to. Congruence makes it clear it pairs with "house" in this imagined language, marked by roman lowercase numerals picked at random. We can now imagine that Q pulls along pertinent 'factors' along with it:
Q.iii red.iii you saw house.iii?
did you see the red house?
Verbal interrogative markers seem somewhat more likely to be discontinuous - just consider the English polar question.