I didn't think sportsmen used jock straps anymore. All the professional footballers in our country use briefs or compression shorts. My experiences with jockstraps when I was young were not pleasant, and I quickly decided briefs were the way of the future.
Frankly, I think Tim would be ill-advised to even consider a jock strap (the male version of the g-string perhaps). He really does need to experiment a little with the bike shorts he has, and consider buying other pairs until he finds the brand and model that best suits his anatomy both in terms of chamois and support.