Are there any smaller boxes for updating to 200 amp service than the 36" X 18" standrard box my electrician mentioned. This box would have to be installed in our master bedroom as we have no basement and the existing 100 amp box is in the closet, where he cannot legally install the new service. If I could find a box smaller than 24" high by 20" wide, it would fit nicely behind a framed picture. Thanks...

There may be a smaller box available, maybe with less breaker spaces. Shop around a little bit.

Also is it possible to install the new panel outside? I would go outside if the old panel is near an outside wall or if the wires wouldn't be that hard to rework to that location.

Most panels for residential are 14" wide, to fit between standard stud centers of 16"OC, so not sure where your electrician is coming up with 18".

GE makes a 200 amp panel, with main breaker, and 42 circuits at 14" wide by 28-7/16" long. They also have a 32 circuit 24-11/16" long. I don't think you will be able to find anything smaller.