I see your red line which I'm assuming is your p propose cut line.
I don't recommend trying to cut it that way. It will complicate your cut big time.
If you cut the top off even with the horizontal board that divides the cabinet, it will be far less complicated. You could install a piano hinge at the back and a support to hold the lid up when raised.
Your working with thin veneers and your glue is 80 years old. Any resistance and the veneer will start to delaminate.
I would start by taking the back off and removing all the guts of radio. You may find that the top of the the cabinet can be unattached from the lower cabinet without any sawing. That would be to good to be true.
Good luck and Keep us posted.
If you don't have time to do it right the first time, when will you have time to do it over?