If you pay close attention, yes you can hone with the crank still installed. Your just doing a light hone for the new rings.
If you want to pull the flywheel and crank, as posted above, a puller is best.
In a pinch, you can put pressure between the block and flywheel (lifting the block slightly) and smack the "flywheel end" of the crank (use a piece of aluminum in-between so you don't damage the crank end). It should pop off fairly easily..
Once the pistons out, carefully remove the old rings and measure "ring end gap" for the compression rings. It'll give you a good idea how worn they are.
As for replacements, I don't know what / if Briggs offers oversized rings.
Worst case scenario, STANDARD new rings will be considerably tighter than the old ones and very possibly within specs
I don't have the tool for measuring the bore however you can again, get an idea measuring between the bore and piston itself to see how worn it is.. These engines will run darn near forever if even slightly maintained
* An old Dodge slant six engine I acquired from a friend would blow 5 quarts of oil out the dip stick tube within 10 miles or so.
Pulled the motor, ring end gap was 1/4". Replaced the rings (STOCK SIZE), (didn't even do a valve job) and it didn't leak / blow a drop of oil for years (BIL bought it). Compression was blowing past the rings, into the crankcase, then out the dip stick tube.