Yes, I think he would have back spatter on him - at the very least. He would have hairs from Nevill and Sheila on him, probably. I think DNA was in its infancy at that time and not used routinely in police investigations, so he probably wouldn't think about that specifically (though he might have done, as it may have been discussed in TV programmes, etc.), but it's just normal intuition that he would want to either dispose of or clean whatever clothing he was in and change as quickly as possible. I also think he would give some consideration to what would happen if he is caught outside Bourtree Cottage and he would not want to be seen carrying a rucksack or bag - and he certainly wouldn't want to be seen with a bike (how the hell would he explain that?).
Of course, Jeremy has carried this out thinking that it would be easy and he could kill them all in their beds, maybe in their sleep, so possibly he doesn't bring a change of clothes with him and he has to improvise and maybe take some of Nevill's, and a bag from the farmhouse to carry them in.
He must need a change of clothes. Otherwise, how come he exits without leaving a trace? How does he manage to get the silencer into the gun cupboard without leaving any blood marks in the den and the cupboard itself? How come he doesn't leave blood prints on the doors and walls and stair banisters? He has obviously washed himself, maybe showered there, and changed, before exiting through the window.