Bob - The LP4-3 rivets Van's use on the RV-12 are manufactured by Gesipa and called PolyGrip Multi-Grip rivets. The Gesipa part number is GSMD41-43APG. The specifications on the rivets are a minimum shear strength of 162 lbs. and a minimum tensile strength of 236 lbs. That is from their online catalog available as a PDF download … mine is dated 2009. The grip range is .039 - .197.
I have been assembling my RV-12 with the flush rivet equivalent from Gesipa that are the countersunk version of the LP4-3 rivet Van’s uses … all the specs are the same except they require dimples or countersinks in underlying surfaces … in your case 120 degree dimples in the skins and ribs along with 120 degree machine countersinks in the spars. A whole lot of extra work. The Gesipa part number for the countersunk equivalent of the Van's LP4-3 rivet is GSMC41-43APG.
I would imagine you may be able to use the Van’s CS4-4 rivet ... however you would need to do a little research to see if the minimum grip range of that rivet will work for you. The ribs and skin are .040 and guessing the wing walk adds another .025 or so (not near the project so sure how thick it is).
If you decide to go with the Van’s CS4-4 rivets, suggest using Cleaveland dimple dies and if you go with the Gesipa rivet suggest using the Avery dimple dies. There is a small difference in the head diameters of the two rivets (CS4-4 head is a tad smaller). I found the Gesipa rivet heads sat a little proud with the Cleaveland dies and were perfect with the Avery dies.
If you do some keyword searches on my build site there are photos that show the dimple die issues I discovered. Not all that long ago I had a post titled "Not all dimples are created equal" ... or something along that line.
Hope that helps … happy building.