It isn't as bad as you may think, cngodfather.
First, Honda's service limit for GX160 ring gaps (for when you are checking used parts for re-use, or re-ringing without boring oversize and fitting a new piston) is 0.040" for all rings, and you are well within that. I have found with another small Honda engine that oil smoke does not appear until the oil ring gap is rather more than the 0.040" limit.
Second, some replacement rings routinely are made with smaller gaps than original equipment rings, so they will work satisfactorily in fairly worn bores. I was once re-ringing a GXV120 that had 0.007" of bore wear, and I found a set of cheap aftermarket rings from Thailand that gave me gaps ranging from 0.015" to 0.017".
