yea you can use a scope probe, as it is a metal probe with meg-ohms impedance on it, and I have once, but I have some cheap Chinese 17$ free shipping ones, some 50$ + a pair HP or Tektronix I would bee leery about

you could use multimeter probes but then again probes in those nice plastic grips cost money and there is no advantage to most el-cheapo ones

long handled plastic grip screw driver and a length of wire wrapped around it will work, add a big resistor and it wont pop, or just let the thing sit unplugged for a while AFAIK (and someone will dis / prove my claim) its got a bleeder resistor built in that ties the 2 to ground so if left alone it will slowly even out (discharge)

if you choose to rapidly discharge your crt, do it on the ground lugs on the front of the screen, don't do it on the chassis, they are separate, and discharging a fresh crt into the logic ground can cause issues (like death of computer)

the second scary thing is implosion, this is easy to avoid (and I have been pretty loose in removing them), just keep a watchful eye of things that stick out, and remember the neck is fragile, the front is thick and heavy, so support it from the front and avoid banging it into anything in the back