Your idea to use shims on the ends will work fine. No need to get too critical on how they are made. They can be 1/4" all the way through or they could be tapered.
If I may make a suggestion, if you left the end that will be shimmed lay on the beam to be shimmed and set the other end with the joist hanger, and nail the center of the new joist, once it is roughly in place, so to speak to the existing joist. Te joists when finished should be nailed together with 4 nails every 16" +/-. Back at the center of the span.... Nail 2 groups of nails to attach the joists together firmly for now only as part of the finished product. Once those 8 nails are in, then shim the end with the shims you choose. This will "pre-load" the joist so it is already taking on some of the load the floor has and will not need to allow the floor to sag anymore before it takes on it's own load.
FWIW, you will enjoy the idea of the joists being slightly smaller than the originals. Since the floor system will sag over time, that process make it quite difficult to install new material beside the old. You still may have to drive them in with a block of wood to protect the new joist from being damaged by the heavy hammer. Lay the new joist in so the top is leaning against the joist you wish to sister and drive in the bottom to meet it fully. Nails going through the subfloor above will give you a hard time if you don't get them out of the way too.