It hasn't been established (as far as I know) that the family had connections with travellers, however, travellers are not all decent people, indeed they have quite a reputation for crime etc. Couple this with the fact that SH has over 30 convictions AND the proximity to Layhams Farm Road AND a trip to the funfair (when it's assumed he knew TS was dead) and it makes a great deal of sense.
On top of this if by this time CS was aware of the body (and perhaps if she wasn't) and it needed to be moved, what better way than to ask a traveller friend to help move the body in a car that is unlikely ever to be forensically tested?
Oh, and then he possibly felt he had to tell the world they went hunting in a funfair to find TS, (when there are plenty of more likely places a 12 year old girl could be....) as it was likely the car was on CCTV?
I'm actually convincing myself now......;-)