UKC

Can anyone please recommend a hard shell coat with a hood that does not accommodate a climbing helmet? 

Thanks

David

No, I couldn't recommend one like that, rather I'd recommend a hardshell that has some sort of adjustment to the hood to keep it anchored in strong wind), or probably better... refer you to "breathable waterproof jackets" instead (which are the same as "hardshell" but at least £200+ cheaper)

I find my Crag hoppers jacket the breathable material performs very well, some of their range like £65 https://www.craghoppers.com/mens-waterproof-orion-jacket-falls-blue-1/ actually have traditional chunky zip and external storm flap, not the stupid waterproof zips that jam and break as per current fashion. My similar jacket, struggles with helmets which you seem to desire, it can just manage a Petzl Meteor with no lights but an ecrin roc with underground lighting fitted is a real struggle

try Craghoppers, they're actually pretty good! Not for Arctic expeditions, extreme alpine etc, but for an ordinary outdoor jacket fits the bill. Go bigger to accommodate winter clothing if that's your use

Maybe a running or cycling specific jacket? Most can be adjusted fairly well to suit different head sizes.

Probably stating the obvious but some people use a baseball type peaked hat (or a peak alone) under a hood. Recently I've used a balaclava over my Buffalo hood to prevent it being too loose and obscuring vision ( looks silly but Buffalo users should be immune to derision ). I suppose beanies or even a helmet on top might also work.

Anything geared towards general hiking instead of climbing would have a somewhat smaller hood but even those tend to be roomy to accommodate down hoodies or warm beanies. 

Arc'teryx's Zeta line and Fjällräven's Keb Eco-Shell Jackets come to mind as models that might fit a helmet when necessary but are not built for it. 

The best hood is a hood that is really adjustable and in such cases even helmet compatible hoods are not a nuisance. 

I think Montane sell a couple of waterproof jackets without helmet compatible hoods. Look at the levity and gravity models.

Adding to Victor's comment, I believe the Arcteryx zeta jackets are discontinued now and are being rebranded under the beta line. Unless you can find some old stock for the zeta, the new equivalent is the beta jacket I believe. As always, very pricey

How tough would you need it to be?

Running jackets like the Inov8 AT/C Stormshell could fit the bill if lightweight would work.