No need to "risk" anything-- contact the Hilton directly and ask them if they'll honor your Diamond status if the booking is made through BA. If they say no, you can then decide whether the cost differential of booking separately (your option 3) is worth the lounge and breakfast compared to booking a different property. If Hilton declines, you can ask the same question of Radisson.

If you're considering the Hilton Old Town Prague, it is one of my favorite properties- great lounge, location, restaurant breakfast. They were very good to me as a gold- I'd definitely ask them before doing anything else.