Absent a CRT tester, you can at least test the filament for continuity. In this article, scroll down to "Checking Tubes Without a Tester:"
http://antiqueradio.org/FirstStepsInRestoration.htm
In this section are a number of articles about restoring various old TVs. None of them exactly matches yours, but you can see what's usually involved:
http://antiqueradio.org/restoration.htm
This article has general info about replacing capacitors, if you need it:
http://antiqueradio.org/recap.htm
Regards,
Phil Nelson
Phil's Old Radios
http://antiqueradio.org/index.html