You can try EBay for the shaft adapter. I have never tried to use one. I presume the old shaft is either 25mm or 1"? Why wouldn't you just buy another engine with the identical shaft dimensions to what you have now?

You don't say, but I'm assuming your existing shaft is 3/4" and the new Predator has 5/8". Granger, among others has what you need. They are about the least expensive at $2.50 each when bought in three-pack. See below:

Here is a link that might be useful: Grainger 3/4 - 5-8 reducer

Do you have the impeller off the engine already? The reason I ask is if you end up destroying the impeller, they may offer another impeller with the shaft size you desire. I've run into that before. Not that hope your impeller gets damaged .... :)

IIRC, the Predator has a 3/4~19mm . I lucked out when I replaced the Tecumseh on an old Ariens snow blower. I used the same pulley,