Hello cheeryface.
Please make sure you do a proper test, i.e. your dcs spend some time with guinea pigs, before you buy them.
Both my dcs have pet allergies and you can't always predict them! My ds doesn't react to my friends long haired cat, but we have investigated both Devon Rex and Burmese cats as potential pets, both of which are meant to be least allergenic, and within an hour he had streaming nose, sore eyes etc.
My ds (who doesn't appear to have asthma but does react to some chlorine swimming pools etc. ) held her cousins guinea pig for a while and her breathing went strange, with extra breaths.
It would be unfair to keep them in garden and then not be able to let your ds cuddle them for any length of time. So please do some considerable cuddling first.
There is a product 'petal cleanse' which is supposed to help reduce any effects.
Also (you can tell that i have been down similar routes of research as you) if you look on net you will find that many people DO react to hamsters.
But also, with both guinea pigs and hamsters you have to think about the hay/straw/grain aspect as some children (and adults) who are sensitive can react to them, or the dust they give off.
Sorry, don't mean to sound pessimistic - I hope you find an answer (we now have a tortoise! Expensive, has to live in vivarium, not very cuddly but no reactions!)