unfortunately your napping days are comming to an end. I hae 5 kiddos, my older three being above the 3 year mark and each of them cycled out of naps during their threes.
It is hard because they are indeed a mess come 5 pm but that is just part of growing up.
In our home we still require quiet time. You don't have to sleep but you do have to stay on your bed with your 4 books and a few specials (small stuffed animals)
Normally what would happen is we would have a few days of no napping and a few days of napping.
Many nights of the no napping stage we had early bed (between 6 and 6:30 instead of the usuall 7) and/or things just ran different like- bath time before dinner. Baths usually bought me more time and cheered up the grumpiest kid!
LIke I said it is part of the procdess of growing up. Don't fight him over sleeping- you will end up 2 very unhappy people and the majority of your day will be wrought in frustration over him always being "in trouble" for not sleeping. INstead change things around and in a few months he will start to adjust. Some days will be sleeping days and some days won't.
I WOULD however require quiet time. He must be quiet and he must be in his room/on his bed (My kids did not graduate to non bed status until they could be responsible about being quiet with their toys during nap time). This way he still has down time and you can still nap with your younger one if need be.