Determining timeout draw in small rapid tournament OTB

I’m helping organise a tournament for kids that’s coming up soon. We have 12 players signed up and we have two hours for the whole tournament. The games will be 10 minutes no increment. I have only just realised that following the FIDE rules for determining when a timeout is a draw could be quite time consuming. Therefore I think I will need to use a simpler rule. Here are two possibilities that have occurred to me:
1. The player who times out loses regardless of material.
2. The player who times out loses unless their opponent has only a king, a king and bishop or a king and knight (in which case the game is a draw).
I was wondering if anyone who has experience with this sort of thing could suggest which of these simple rules is better or suggest a better simple rule. I don’t believe we will have time to check if there is a possible mating sequence in situations outlined in case 2 above.

First, highly recommend following FIDE rules : they are the standard for a reason.
Secondly, the difficult / " time consuming" positions are extremely unlikely to occur. Good odds you won't run into any such cases with 6 games each round. Most of the time someone will have a pawn, so it's easy to see that there is a way to promote, and a way to checkmate. That, or they outright have mating material already. Really, the one thing to watch out for is forced lines and (kinda artificial) fortresses (ie. the examples here chasolver.org/examples.html ) And keep in mind a lone knight can checkmate if the opponent can block themselves in a corner.

As a bonus : you can even use this tool github.com/lichess-org/lila/issues/9249 / chasolver.org/analyzer.html

Thanks so much for your reply. That analyzer is very helpful. I realise that I’m worrying about some unlikely situations, but I just wanted to be prepared.