J wrote:
Greetings!

I'm building a snake box for my rca gear. I'm going from rca female on the
box to a multi cable and probably back again and I can use a panel-mount
rca, solder a shielded (or unshielded?) wire to an output connector (below)
(db 25).

Yes -- there are db-25 type connectors with coax fittings for 75 ohm, so
you may need baluns to do this properly. I wouldn't use RCA type
connectors for this purpose in any case. They're really not
sufficiently well shielded and you can't lock them in place.

What about a Double shielded twisted pair DB25? if not please recommend an
available cable/connector.

If I use plain unshielded cable inside the (metal) box, could I run into
problems?

You're going to have lots of different signals inside the box, right?
Shield. And be sure to ground one end of the shield.

Do I have to worry about shielding, say, composite video from component or
audio (-10 or +4) inside the box?

No need to worry. Just do it.