So when the cyclist gets within, say, 2 meters of the vehicle's blind-spot they are alerted by the wristband.
The only way I could think of doing this would be to use a projector with an IR source, projecting a beam the size and shape of the blind-spot.
However, I can't think of a good way of stopping adjacent vehicles, or vehicles going in the opposite direction giving false triggers.
RF isn't going to work.
Perhaps you could design an advertising campaign instead, educating cyclists on the dangers of riding in stupid and dangerous positions.
(Aside: you expressed a budget in pounds, yet spelled "metres" as "meters" - where are you?)