Honestly, that's probably the shutter that lens is going to be fit unless you want to pay to get it remounted into a modern shutter (or get an adapter made etc). When you find out how much that costs you will be back to looking for a No4 Acme shutter...
That's a nice shutter, I have used Kodak film cleaner as solvent, lube all in one. Great shutter.
I have a 1959 version of this lens (Serial #RY 336) mounted in a Compound Shutter. Not sure which size Compound shutter: below the lens, the shutter states: "D.R.P. COMPOUND D.R.G.M.". On the dial with the shutter speeds, it states "D.R.G.M. No 371939". This Compound shutter seems to be the same size as your Ilex #4 shutter. My Compound shutter only opens to f5.3, not f4.5. Otherwise, it works fine.
If your shutter is not working, then try contacting Carol Flutot to get it repaired or CLA-ed.
Daniel
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