Hives from contact are quite common.
Our son regularly had hives. from all sorts of situations, from wriggling under the bed ( dustmite) or full body hives from running naked under the trees (pollen) or hives in the car, this was if the heating vents were pointed in his direction( again pollen)
At one stage removed egg from home as he had hive reaction when he stood next to me in kitchen as I fried one!
Now he is able to eat cooked egg. So bare in mind that things do change. Allergies seem to change rapidly as they grow older. They dont all go, but some do.
Hives as an only reaction are not serious, its a pointer to observation in case of other symptoms.
Which you may already know.
Pre-school IS possible. look around all in your area, and chat to each leader and choose the one who is more open to your sons situtation.
They will more than likely these days to be 'allergy aware' certainly they will have come across nut allergy. They may not have of had experience of a child like yours with multiple allergies, but many have had training in epi pens .
The two main issues are food, cooking, and snack time. A management plan can be arranged to reduce the risk of a contact reaction and reduce the chance of anaphylaxis.
the anaphylaxis campaign do have a schools link,
www.allergyinschools.org.uk and they feature pre-schools.
I think it would be helpful to met other parents who have a child like yours, it certainly helped us.
Try the anaphylaxis campaign , and go to the parents workshops or the family fun days. Or even see if there is a support group in your area.
if you want I am happy to talk to you if you want.
just so you know , my sons allergies are to date ( he is 10 now , they have changed, lost some, gained some diffrent ones!) peanut/all beans/egg/kiwifruit/marmite/bovril/dog/cat/tree pollen/hay fever/dustmite
Some antihistamines, some ezcema creams etc etc.
hope this helps.