A 300B, no, 10 watts is pretty much the max unless you run it into A2, or up the max limits, but I don't think most of the current production ones will take that kind of punishment. A 211, 845, GM70 or triode-wired 813, no problem. You just have to be prepared to deal with 1000+ volt power supply. If you're not an experienced DIYer that's a risky proposition. Also, SE amps with big transmitting tubes get complicated, expensive and heavy. You need a hefty DC supply for the filaments, and ALL your power components, including wire, caps and resistors, power tranny, chokes and output transformer have to be rated for transmitter level voltages.
That said, it can be done and a lot of people have, but it isn't cheap or easy. I have built SE 845 monoblocks, twice, for friends. By the time I was done I had no desire to do it anymore. ;-) I'm now a PP guy pretty much for that reason.
If this doesn't seem doable for you, consider a PP 300B. You get a good dose of the 300B sound with the advantage of more power, better bandwidth, better speaker control, quieter operation and cheaper components. It's a very good sound. I'm working on a PP 300B Williamson amp right now and pretty much have it nailed down, just waiting for some more components. The only downside is the price of 300Bs, but some of the Chinese ones go for $60 and aren't half bad at all. That's about the same as a KT66 these days.