No need to change over to that electrode size for welding that thickness or to anything more than thoriated. Yes, it is a very slight radiation hazard, but its LESS dangerous than the old swiss army watch or the cell phone you talk on. It emits alpha radiation, and that doesn't penetrate the skin. Just don't breath the dust, which you'd be hard pressed to do that.

3/32 will handle the heat range needed to PROPERLY weld those thicknesses.

A properly welded joint of 1/4" will have two passes made. You'll only need about 70-80 amps to do it. There are many reasons for that, but guys trying to "burn" it in all the way through on something like that create a large heat affected zone, creating brittleness at the edge of the weld. Also carrying a large puddle helps trap impurities such as slag and oxidation in the weld because the puddle begins to cool on the top before the contamination can float out.

The REASON you need MORE amperage is for thicker materials that require more heat input because the metal is large or thermally conductive enough to "suck" up the heat faster than it can be put in.