Well, a 24"/f:11 lens needs to be at least 2.18" in diameter plus a little room for the flange, and the maximum iris on an Ilex #4, according to this chart:
is 1.730", turning the lens into an f:14 lens, presuming that the lens and shutter can be machined to fit (probably can, but ask Mr. Grimes). So you lose about half a stop, but you get a smaller, lighter shutter.
What I've done is to take the Ilex#5 shutter that came with my 10" WF Ektar, and I've had an adapter made so that by removing the cells for the Ektar, I can mount my 12" Dagor or my 19" Apo-Artar onto the front of the same shutter. The shutter is big enough to work in this way without causing any vignetting with these particular lenses, it means I have fewer shutters to maintain and more consistent shutter speeds from one lens to the next, and that's only one big shutter/lensboard combination in my pack for three lenses. The downsides are that if that shutter fails in the field, there are three lenses I can't use (hasn't happened yet!, and it takes slightly longer to switch lenses if I have to swap out the cells for the Ektar to put on the 12" or the 19".
Personally, I'd hold out for a #5 shutter, if you think you might want to use other barrel lenses on the same shutter. If not, go for a #4. Mr. Grimes often can provide refurbished Ilex, Alphax, and Betax shutters himself at reasonable prices. Have you asked if he has what you need in stock?