Bob,
The set is designed to work without the remote control. You will need to have the spherical mirror (in the bottom of the "tank") resilvered. The guy at Spectrum Coatings dose an nice job at reasonable prices:
http://www.spectrum-coatings.com/
The flat front-surface mirror in the lid should also be replaced for optimum performance (brightness). Front surface mirrors can be purchased on-line, and a local glass house can cut it down to the trapezoidal shape required.
Check you 5TP4 CRT for emission. If weak, look for a NOS replacement. They go by on ebay every now and then, or maybe a collector has one to spare.
Once you have recapped the set, note that the power supply and video chassis can be run on the bench stand alone for troubleshooting. Likewise, the horizontal/HV chassis and power supply can be run stand alone on the bench, though you will need to clip lead in a temporary horizontal hold control.
Then you can put it all back in the cabinet and hook it all up for final testing and adjustments. I would not recommend setting up the optical barrel on the bench, it is a lot of extra trouble to do so, and you don't need the potential x-ray exposure. But with the optical barrel in the cabinet, the x-ray exposure is minute.
The audio chassis is known to have that rotten rubber covered wire in it, so be prepared to replace some wiring. I would also recommend you replace all the chassis mount wirewould resistors with more modern replacements. The chassis mount resistors are notoriously unreliable.
One it is all tweaked up and working well, you will be surprised at what a bright picture it has.
Good luck and have fun with it!