This is something that I've been trying to hunt down for for 25 years so I'm not sure how much use my input will be.
what size game are you looking for? What table size and how many mini's per side?
As Mick has said Lion Rampant is a great set of rules and a
lot of fun. I don't think I've ever played a LR game without plenty of requisite guffawing and rolling around!
If you're looking for a medium size game, say 100 mini's per side then Never mind the Billhooks, free with Wargames Illustrated 393, is looking excellent. I say looking as I have not been able to play a game due to the Covid restrictions etc etc.
There's a NMTBH Facebook Group where ideas are sometimes being banded about for other periods so it might be worth joining the group and seeing what is what.
You ought to be able smoothly convert/amend NMTBH to the HYW without much difficulty.
There's also a set of rules called Pig Wars, an excellent skirmish game meant for the 'Dark Ages' and our group converted it for use for the HYW and had some killer games. I don't know if Pig Wars is still available but an online supplier of pdf's such as Wargames Vault might have a copy. I would send you the amendments but I fear they are lost in one of my old steam powered laptops