I play on offline Minecraft and I'm stuck with the Alex skin for 1.8. I have a custom resource pack that changes my skin but it still has the small arms. I was wondering if there was any way in game offline that I could get the 4 pixel wide arms instead of the 3 pixel wide arms. I'm playing in 1.8.8.
This, unfortunately, cannot be changed in-game as far as Vanilla Minecraft goes. To change from Steve or Alex, you will instead have to go on the Minecraft website, log in, and enter the Profile page. From there, you can choose to have a skin that fits Steve (though if you don't want a skin, all you need is to switch to Steve and Save).
NOTE! THIS ANSWER IS OUTDATED. IT NO LONGER FITS THE QUESTION
There IS a way!
You can make a resource pack that changes the look of Alex (or Steve)!
download the recource pack here: http://www.mediafire.com/download/h0rw97kwaa12u0m/alexChange.zip
unzip the file, and navigate to the folder then to assets->minecraft->textures->entity
in this folder, paste your skin file. if it an Alex skin, name it "alex.png". if it Steve, name it "steve.png".
Move the entire resource pack to your recource packs folder in your minecraft directory.
remember that if you go on a multiplayer server, all players with no skin will show up as your skin, so remember to switch resource packs!