I very highly recommend you take it to a semen distributor, bull stud or somewhere else that has the big tanks where they can take out each canister and see what's in it. If not that, then get a styrofoam ice chest and some extra nitrogen you can pour in it, at least 8" or so, especially if you plan on rearranging individual straws. Every moment that semen is above the neck of the tank or higher it's at risk of damage to semen quality, and that risk rises proportionately the longer it's exposed. Add to that the fact that alot of the semen we deal with nowadays has a much lower count to begin with, and I just think it's worthwhile to spend a little extra time and money to do it right.
Before you go through all of that though, first I'd try quickly pulling up a cane long enough to read the code and make a quick count. Make a list of the codes you don't know and post them here - I believe there's a site or two on the net with quite a few codes listed, and between us all here, there's a very good chance someone can find it in their records. If you want to move canes from one canister to another, use a second tank and move the cane quickly to the other tank, then get the canister ready that you want it in and quickly move it back. As Chris says, two people are an absolute must, and a third to do the writing would be great. It's best if your tank(s) are full of nitrogen, because the neck stays colder and there's some nitrogen in the goblets themselves. Always raise the canister into the neck just high enough and just long enough to do what you have to do, then lower it back down into the tank. I personally think the risk of damage in moving straws to the lower goblet without having them in nitrogen while you're doing it outweighs the slight advantage of decrease in temperature it gets you.