Which way to go...

Are there any types of traditional astrology that don't use houses?

Not really, no.

Ptolemy didn't really write about a house system or houses at all, focusing mainly on the four angles, but his dislike of houses was very unusual and unique to him due to his feelings on the Egyptian mysticism from which the houses arose.

as mentioned by our follow community member the concept arose later but there are normally no such traditional astrology that goes without the course of houses