Nick, I have both types, my Thornton Pickard shutter works fine with a Wray lens designed to cover 8”x5” which is approx 12”/300mm FL, and covers that format without vignetting, and I think would be just OK with an 8” lens on 5”x4”.
All the Thornton Pickard/lens combinations I've seen tended to be longer focal length Portrait lenses.
However the Packard shutter as Whitey says can be fitted closer to the rear elements and I can use almost any lens from my 151mm f16 WA Ross (Protar) lens upwards on my 10x8 cameras with no issues. But in your case a 5” shutter would give a better safety margin, but in practice a 4½”
might be fine as your only covering 5”x4”.