Towing through Fishguard

During July we'll be visiting St Davids then moving up the coast to New Quay, and without what looks like a large diversion it looks like it will involve towing through Fishguard. Having looked on streetview it looks like there is a narrow bit heading northbound starting with the bridge over the river and continuing to the top of the hill. Has anyone used this route, and if so is it OK? or can anyone recommend a different route?

Thanks