Among the preliminaries, clean all the pots and don't overlook the service switch, which tripped me up once. While you have each tube out to test it, clean its pins with very fine sandpaper or whatever you prefer.
Re the 6AU4/6DE4 replacement, the Nostalgia Air database (
http://www.nostalgiaair.org/Tubes/ ) lists 6DE4 as a sub for 6AU4 (with an asterisk) but not vice versa. You can also look up data sheets at a site like
http://tubedata.tigahost.com/tubedata/ for more details.
I'll let smarter people advise you when & how to apply power (perhaps with HOT pulled, for instance?). My advice is usually to replace all electrolytics before powering up, but I've been known to bring up an as-is set on a metered variac to see what happens, so do what I say, not what I do
The HV cage has a circular cover that you can slide open to peek at the flyback. One of my CTC-11 flybacks has dripped a fair amount of wax but the set has played trouble-free for many hours in that state, so dripped wax alone isn't a death sign. If it doesn't look completely burned up, I'd assume it's OK for the moment.
Phil Nelson