What's your dumb trainer?
Some dumb trainers are very accurate when used for virtual power, most are dubious. The Kurt Kinetic fluid resistance unit on their Road Machine, for example, is very usable for power training. They're also bulletproof, so if you can get a cheap one second hand from someone going to a smart trainer, you'd be well equipped to use Zwift, Trainerroad or similar.

HR is in my opinion very useful when cross referenced with perceived effort and as long as you use it sensibly.

ETA: It's not necessary to have power data or HR data available during your race to benefit from it. It's in training that it's most useful IMO.