My dad had a need little mono 6l6/6v6 amp from when he was a teen that would have been perfect for this, but it has not been seen in many many years,
It has to be someplace, as I highly doubt he got rid of it, it's most likely hidden in some deep dark corner in the attic above the garage waiting to be found mixed in with all the tons of other strange junk he has up there.
I guess the quickest, easiest way to go (for now), is to get a cheap small class D amp, about 10 watts, and use that until I find / make something more appropriate, (find my dad's amp, make something from scraps, or find a cheap used.) however, by combining a early 50s era vintage TV with modern era amp technology, I run the risk of causing a rip in the rip in the space time continuum, and destroying all reality as we know it!
moving on,,,
Replacing the paper caps...
Paper caps have polarity, as they are clearly marked on the one side for the filtered /low side, and the film ones to replace them for the most part don't , example, the Panasonic caps have no polarity markings, though I have seen SOME film ones with a black mark on one side, where one can assume that is to go to the low side, like the paper was in originally... the info out there is confusing.
Also, the new caps are much smaller than the ones being replaced, so I would be safe to assume that it's best to put them closer to positive source, and have a longer lead on the filtered (what was on the black stripe side on the old cap), than to have it the other way around?