Another solution could be to develop the Blue Steel 2.
That is another option.
The Skybolt seem to be unnessary for US and this is the problem. Why fund a missile you do not need?
But the Skybolt worked well? if yes, what about Britain continued its developent alone?
Skybolt put another type of weapon in the SAC quiver that would have been difficult to defend against (same issues for defense as Polaris - distributed and uncertain launch points, and ballistic trajectories that take a different type of interceptor vs. ALCMs). It's not out of the question to come up with an alternate history where they get deployed - especially if you can keep the B-70 around - it give the Valk a long range stand off weapon when it's limited to 14 foot weapons in the bay (look up the geometry of the doors at some point for why this is).
Could the Hound Dog "britisized" with british engine at least?
Of all of the ALCMs, I'd give the Hound Dog the best chance of such a modification being workable
Also Britain could develop an ACLM of its own, RR had several small jet engines to power it in 1960's.
Yes, but that gets expensive, which is the problem with so many of the UK strategic programs. They just don't have the sheer piles of money that the US threw around.