You can find 10" "flatscreen" monitors out there, but you'll have two problems to overcome. The flat screen won't fit the very curvy bezel that housed the very not-flatscreen Sony Trinitron CRT.  You'll have to make up the difference somehow.

The bigger problem is actually finding a 9" or 10" monitor made in the last 5 years that has the proper aspect ratio. 4:3 monitors are still made for some specialty applications, but most everything you'll find easily will be 16:9 or 16:10 ratios. The ones I've been able to find that are in the right size range and 4:3 tend to be more expensive than I'm interested in dropping on the project.