Behold, author signalled from keyed 4-1000A filament:

The power supply in my radio has audible hum in the background and
bypassing the diode rectifiers with capacitors does not eliminate the
hum. There is no hum when using battery power. The solution is to build
my own power supply. Does anyone have a design for a compact 6V supply
that I could build for this purpose?

Indeedy I do!

http://geek.scorpiorising.ca/schematics/6vFilPower.png

Origionally designed for tube filaments, but will suit your purpose just
fine :-)

--
Gregg
*It's probably useful, even if it can't be SPICE'd*
http://geek.scorpiorising.ca