I have a 1/8 bit that is 12 in long, you should be able to get them at ace hdwr. I also have a couple of 1/8 wood chisels (mine are both antiques, but Marples still makes one.)
you are using a 3/4 wide tang. about an inch below the ricasso let it taper down to about 3/8 inch. Draw the temper at the ricasso dark blue, and light blue below that. It should be plenty strong enough to hold a handle. If the blade is small you can safely tak the tang down to 1/4 or even 3/16.
I always cut the mortice first. then shape the handle If the end of the mortice is ugly add a butt plate and a bolster, and assemble it with epoxy. You won't have eny problem. If I am building up a handle out of many layers, I actualy cut a sloppy hole and assemble with epoxy. I shape the handle after glueing. I've been doing this for years, and never had a problem. (the only problem is getting one off if I screw it up

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If you must have a mortice that size, that has a good fit at both ends. I recomend that you shape after you cut the mortice. (it is much easier to clamp a square block. drill through first then lay out your mortice, in case the drill wanders. cut from the top down half way. then turn over and go at it from the bottom up. If the inside gets a little sloppy, well there's always epoxy. when cutting a mortice you should have 2 chisels, in this case one 1/8 in. and one 3/4. the problem is a 3/4 in. chisel that will fit in a 1/8 wide mortice that is 4 inches long. you will have to improvise something from 1/16 inch stock.
An acurate mortice that size is no easy thing, especialy into woods like rosewood, and then intoend grain at that. I know a lot of good cabinet makers that would refuse to do it.
have fun

EE
(the cabinet maker in the crew)