Swiss Tournament

Does anyone know the best way to run the pairings of a non rated Swiss tournament that is somewhat casual? We ran one already and relied on the players to give us their estimated rating. Most players weren’t FIDE rated although a couple were and some who weren’t were still very good. There were also some mid level players along with some novices. We think the pairings worked out ok and everyone had a blast. But for our next one I’m wondering if there is a concern with relying on the players giving us the rating. Could a really good player lie to make it easier for them to advance? By what I’ve read that would be a gamble cause they play someone in the higher bracket first round if they rank themselves too low. Or could a bad player say they are very good to play a lower bracket player in first round? I don’t think that would really work out for them either cause they’d play someone of higher strength in the low bracket. Basically trying to figure out if it’s ok to rely on this or should we just do random pairings? Problem with that is we have big tourneys and only a few rounds so it might not be the most fair.

That is an interesting thing