Whilst I cannot comment on the Suzuki, tyre type, make, or availability, just a thought.
When we acquired our current outfit, the BMW K and Saluki, the rear tyre, mounted on a 15" car wheel, was a 185. Some experimenting with ratios, including bevel drive changes, saw the fitting of a 175, then a 165. Other than slight gear ratio changes that performed as required (well, one didn't, left me with a hardly worn tyre, so don't tell the missus), there was no appreciable disadvantage having the narrower tyres.
More interesting is that the acquisition of narrower Wasp wheels now sees a 145 width tyre on the rear. So far performance remains as required. Maybe, just maybe, the big wide tyres are more about look than anything else.