I don't know specifically about whether it's possible to disable Reporting Services export feature, but I think you can safely tell them it's impossible to make anything entirely view-only. If you can't easily get the data out as data, users can at least copy the screen, or print to PDF, or try to use an OCR program to convert any sort of output back to pieces of data. If your superiors are after air-tight view-only, it's not going to happen.
If your superiors just want to keep it from being convenient to export the data to Excel and do their own easy number crunching, you'll have to wait for someone else to answer. However, if you don't already know more specifics, I recommend that you find out more about what "they" really want to prevent.