Im own the Chipsaway franchise in Nottingham.
There is nothing wrong with doing a repair outside. The materials used are identical to a bodyshop, not every bodyshop repair is done in a spray booth, a lot are done in a workshop floor. Only difference being outside is the weather, dust can be minimal depending on environment and how still the air is, air movement is a good thing to keep dust away. I do on average 3 repairs a day all outside for the last 6 years.
Now there are limits. Bonnets and roofs and full sides are really a body shop repair due to the size with exceptions. On bonnets dust is more likely to settle and it's difficult to cure lacquer off on very large repairs without an oven.
Chipsaway is a franchise so some are strictly mobile like me, some have car care centres and some have full spray booth bodyshops.
On a bonnets it will need the whole bonnet repainting, ie damage repaired, colour blended across the bonnet and then fully relacquered. This would be a bodyshop job so see if the Chipsaway franchisee has a bodyshop.
Depending on bonnet design you can paint to a swage line so it is possible.
Get some pictures up.