No matter what size the stub out is 11/2' or 11/4" get the correct size p-trap the 1" stub out is enough to work with , get your center on the tail piece and the center on the p-trap coming out of the wall the tail piece will determen how far that p-trap will be coming out they'll be the same but in any case you can't awing the trap more than an 11/2" from side to side if needed, but you want it to come out stright for a pedstal sink to look good,
Now what your wanting to do slide the p-trap into the stub out in the wall and measure the center out from the wall to the center of the trap, now mark your trap right at the stub out plus a 1/16" of an inch using a file , now use your tubing cutter and go around the pipe just to mark it , dont cut it off just yet, after you have done that take your file and file off only the chrome thats going into the stub out , now take the correct size cleaning brush and clean the inside of the stub out and on the face of it so it looks like new copper, when your done flux it up and solder it no special fitting needed.
very important protect the walls from the heat and flame
one other thing slide on your escutcheon before soldering it you may have to get a deep escutcheon so it covers your solder joint. good luck !!