> if the 15 Mhz is fast enough to pick up oscillations
You get midrange squeal, slightly supersonic squeal, and very rarely some horribly high MHz oscillation.
99% of my time, a 20KHz 'scope is all I need or want. (I actually built a 19KHz 'scope once: enormous savings in cost.)
The last time I ran into MHz trouble, my 15MHz 'scope would not resolve the actual MHz wave, but the "bursts of fuzz" were reasonably visible. That was a too-tricky chip-BJT amp with (in retrospect) a real urge to sing 14MHz, but only when excited by a lower tone driven near clipping. The 'scope trigger was so hung on the lower tone that the 14Mhz wave would not stand still.
Tube guitar amps "are designed" to pass the audio band... and not much more. You can have high gain or wide bandwidth. Gain is vital. The designer allows "just enough" bandwidth to do the job, so the trade-off favors gain where it is wanted. So MHz oscillations are unlikely. And practically impossible on 12AX7 gain stages.
But possible on power pentodes. They have gain in reserve, and low parasitics. A length of wire looks like a short for audio, but can be a tuned-circuit inductance in the radio bands. Wire-wound resistors of low to medium value are resistors for audio, but can be kinky at high frequencies. I once had a big power-amp go crazy, and traced it to a plate lead run close to a wire-wound cathode resistor. While the OT would barely pass audio, the lead to it could sing much higher, and the coiled-resistor coupled enough energy back into the tube to (apparently) sustain radio oscillations. It took weeks to work out the (possible) theory, but only minutes to solve the immediate problem: Keep Outputs Away From Inputs! (And yes, a cathode is an input.)
> Hope I don't smoke my probes
I've done it a lot. Many probes use 600V or even 300V trimmers; maybe today they give you 100V trimmers.
Most of the time, when you are working above 300V, you are woring on a POWER stage. You really should not be sticking fingers OR probes in power stages. But when you do, build your own probe. Use a 1Meg and a 10K resistor. This gives 100:1 division, so even cheap 'scope inputs can be used with quite hi-volt amps. The 1Meg is no sweat on a 8K plate load. This un-compensated probe is flat "only" to 100KHz, which is less than the 'scope's 15MHz but more than you are ever likely to want to see.