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You may have to look for a pitted up junk barrel, pull the breech plug and have it reamed to a smooth bore. I wouldn't try to go more than a 54cal with a 15/16 barrel .
A Hawkins rifle never had a smooth bore. Suspect the stock on modern copies wouldn't be very good for use as a shotgun either. In any case, I'd rummage around Dixie Gunworks site and see if there is such a thing. Doubt it though.