Hi Carolineno,
A good question!
I’ve watched a small hedgehog squeeze (with much effort!) through a 5cm wide by 7cm tall gap at the bottom of my garden’s wooden side door – quite a lot smaller than the recommended 13cm x 13cm hole for comfortable access! I faced the same question because the side door has a road on one side and a vast green space (gardens and school playing field) on the other side.
Finding out whether the road side of your gate has hedgehogs (eg, using a trail camera) might help with your hole-cutting decision? Also, a thorough check that there are no tunnels or other gaps in your garden walls (perhaps hidden by ivy) would be useful.
My garden has a small population of regular hedgehog visitors but I’ve only seen one instance of a hedgehog transiting the side gate – so I decided not to enlarge the gap (for the same road safety reason as you stated). If you have more hedgehogs on the road side than in the garden then a larger gap might be ok.
Hope you see more happy hedgehogs in your nice safe garden!
Sam_