I should have clarified that. Currently, nobody makes a ER-20 or 25 collet chuck to fit the 3/4-16 thread of the Sherline headstock. The only ones commercially available mount via a MT1 taper so a double-end mill will not pass through that solid taper. I may be wrong but I looked for a long time at these things and could not find one that allows something to pass completely through the body of the chuck, which is one of the major advantages of an ER chuck. This is also why I said you can have one but you have to build one. It has to extend out far enough to hold the end of the end mill beyond the nose of the internal taper of the headstock, which eats up a lot of Z.
Making a chuck should be fairly simple and if you get the rear of the chuck to register accurately to the thread mount it should run pretty accurately as well. You do not need to precision grind the taper but you do have to be able to bore the taper accurately. It also does not need to be hardened, though you can use semi-hardened steel or heat treat it yourself if you like. Lots of these chucks have been made and are in use in hobby shops. The internal threads can be tapped but cutting a large thread like the 3/4-16 is pretty simple. Again, the accuracy comes at the register at the bottom of the thread mount, not the threads. I am not sure of the thread configuration of the commercial nuts but I suspect most of them are metric so you probably have to be able to cut an external metric thread.
One option to all of this is the buy a commercial ER-20 chuck with a large body and cut off the rear end and thread that for the headstock. If you find the right one the only work needed is to cut the internal thread for the mount and then face it accurately. You also have to bore the inside to be sure a 1/2" endmill will pass through. When I get around to doing this I'll probably go this route to save time.