I recap on failure, most of the time. Some scopes I have back to late 1940's caps still good,
even the electrolytics (although I have not actually measured their performance). Decision
depends on equipment. I have recapped from get go SW receivers because of a history of
cap failure.
You should be OK with Hantek probes you mentioned.
It does not hurt to check the scope alignment if you have the gear to do it. I also clean
switches and any socketed parts lift them slightly and press back into sockets. In Tek scopes
they had transistors in PCB/solder thru hole connections, I move them a bit to break any
oxidation. Be careful of HV, make sure you discharge all caps and CRT before you do any
of this work.
http://www.crtsolutions.com/CRTSafety.pdfRegards, Dana.