There’s no problem driving them with your 300 Watt amp, just be careful with the volume control. Again, your ears will bleed before the speakers are in danger.
I have 96 dB / 2.83V Tannoys, and I’ve definitely noticed that noise floor is something to be mindful of. Any power amp by itself, whether tube or SS, should not render audible hiss or hum. The problem is that the amp’s gain will magnify your preamp’s noise floor (from active circuity after the volume control). So the more gain your amp has, the lower you need the preamp’s noise floor to be. Active preamps with a higher gain tend to have higher noise floor, unless their signal-to-noise ratio is also higher. Tube preamps with high gains (> 14dB) are usually asking for trouble. I can really hear the noise floor of many preamps in my system.
The ARC Reference 6 has an extremely high signal to noise ratio, so despite its relatively high 14dB gain, it’s dead quiet in my system. Most other tube preamps, I can hear varying degrees of hiss noise with the volume at 0 (not muted).
In modern times, a SS amp will have higher gain in order to facilitate tapping into a very high power rating (you need a lot of gain to push out say 400+ Watts). However, a lot of the lower powered tubes amps will have a surprisingly high gain because using a 12ax7 V1 tube was popular, and analog sources of that era had low output levels so the extra gain was welcomed (for example: the Eico HF-87 tube amp required a meager 0.38V input to produce full rated power of 35 Watts!). So even when you go to lower power tube amps, it may have similar gain to your much more powerful SS amp. This means you should be very careful if you’re selecting a tube preamp to pair with it, or you will hear its hissssss noise!