[Arran]

Voltage increase is usually insignificant in AC/DC 5 or 6 tube sets.  I'd add a 22 ohm 1/2 watt or 1 watt fusister or better yet a proper fuse to the set.

Only 4 tubes in this radio, three 1 volt and one 3 volt.

No, you need to calculate the proper size resistor in this case, it is much more critical then in a regular AC radio. Each tube needs 1.4 volts, not 1 volt, and the 3 volt one is actually 2.8 volts, too low and the set won't work properly, too high and the tubes burn out prematurely, so 7 volts ideally. If the original selenium rectifier is still working do some voltage measurements to see what the output voltage is before it gets to the filament dropping resistor, and after it.
Regards
Arran