I don't know whether this will help much right now, but there is a standardized lettering scheme,
Speffz which most of us use when talking about pieces. The cube on the Wiki page is a 7x7x7, but if you imagine the groups are just corners on a 2x2x2, then it would work to label a 2x2x2 as well.
Let's take our 2x2x2 and scramble it using: F
Let's assume that your buffer corner is URF. You can choose any corner you want, but for this example we'll use URF.
The piece in URF after the scramble is the UFL corner. Not only that, but the L face sticker of UFL is in the U position of URF. In Speffz the L face sticker of the UFL corner is lettered F. So in the buffer location we have the sticker F.
Now go to the actual F sticker location, LUF, and notice that it is the D face sticker of DLF. In Speffz this is the letter U. So our memo so far is FU. Now we look in the U sticker location, DLF, and we see the R face sticker of the RDF piece. In Speffz this is lettered P. So our memo so far is FUP. Lastly the RDF location has the U sticker for URF. This, in Speffz, is C, which is the buffer corner and we don't memorize it because we know we are done.
So the memo for a 2x2x2, in Speffz, scrambled with the turn F is FUP.
Now you can use your 2 cycle method, or 3 cycle method to solve. Any other blindfolded memorization phase would go roughly similarly. Hope this helps.