Precarve, this might be a lost cause

[Mr. Bubbles]

The thinnest guns are often built with only 1/16" webs, or even less at the breech, and 1/8" at the muzzle.  How thick is your web now?

[Justin Urbantas]

The thinnest guns are often built with only 1/16" webs, or even less at the breech, and 1/8" at the muzzle.  How thick is your web now?

That would be a mighty small tenon. How do you get a pin in there?

[Mr. Bubbles]

It'll be thicker where the tenons go on a swamped barrel than on either end.   That said, you will still need to aim pretty precisely.  If for a pin rather than wedges and you miss by a little (on the high side), your bit will just skid off the bottom of the barrel flat and the hole will be partially exposed in the channel.  Not a big deal though.  Wedge keys are often exposed that way, and grooves can be filed in them to make way for wedge keys that are slightly proud to the barrel channel plane.

[smallpatch]

If you use a 1/16" pin, it works just fine. 

[flehto]

Here's the bbl lug I use for a 1/16" web and a 1/16 dia music wire pin is used.