Originally I was asking if I can drill diagonally at the top of the wall to run the cable to the chase location
Well, you can, as long as the drill bit exits somewhere in a safe zone, or comes out into trunking on the other side.
but I still think I'll have to weave the cable around
Cut the chase in the wall, then stitch drill and chisel out the rectangle for the box.
Then poke a screwdriver up though the plasterboard at the top of the chase, actually inside the chase, as a sort of test hole initially.
Then pull up the floorboard above, so you can see exactly where it will need to go.
Then drill a proper hole through once you're satisfied it's gonna be OK.
I'm 95% certain that it'll be a lot easier than you think, it should only need to move over by about ten centimetres. And seeing as you want the socket higher than it used to be, you'll definitely have enough slack on the cables, whichever direction they come from. The only possible issue would be a joist right where you don't want it. Then, and only then, consider drilling diagonally, do it upward from near the top of the chase, so that it comes out straight into the void under the floorboards, and NOT so it pops out on the other side of the wall. (even though it would be in a safe zone in the top 150mm, it should be avoided entirely IMHO).
Gaz