First take several pictures of the top and bottom of the radio so you know where all the wires are going through from one section to the other.
Next grab up your 1/4" nutdriver and start taking out all those sheetmetal screws.... there is one small part to pay close attention to... at the rear
of the long volume control shaft is a small metal  clip between the end of the shaft and the volume pot... don't lose it...

Models such as 37-610 and 37-630 etc... will take less than ten minutes to disassemble this radio into the pile of stuff your going to see below in these pictures.
Your first one might take a little longer to reassemble all the parts...

Cut and unsolder NO WIRES...    It is Not necessary to do anything other than remove all the screws..
First is a Philco 37-630 chassis... with complete start pictures plus the disassembly process ... later there are pictures of a 37-116 chassis...

picture above... someone had started on this one and quit... I removed the litics hanging there and restuffed the cans with new ones...
in this particular model... there just isn't enough room to just hop in the new litics under the chassis... besides it looks sloppy that way...

Now with the sections rolled up in a ball... and the sides of the tuner section removed... notice that its quite easy to get in there and replace
the old wax capacitors... since you don't want to have to do this whole mess again.. check all the resistors in that tuner section and replace out of
spec ones while your in there... Its also easier to work on the two outer sections with them removed and apart ...

Eventually when you have the old caps all done set the sections back together and start putting screws back in to make it once again
look like a radio chassis...