The Redux Demo version still works on pre-Reforged WC3, but I really don't suggest playing that version as it lacks all features present in the remake version, as well as the fact some of his "remake" works (like Joe's Quest) can only be playable on the most recent version of the game. You can do so through Battle.net to get the most recent version (2.0.3.23101). Purchasing a full copy of Reforged isn't necessary; just use your CD keys from the original copy to download the Reforged "Classic" client.
The latest patch from Battle.net have really good advantages compared to the pre-Reforged ones in addition to custom campaign service, like online play through official server (you can still play against those who have full copy of Reforged), improved hotkeys (although most custom maps and campaigns were made with "QWER" system), World Editor upgrades (you can now make a map with 64 tilesets, which is a nice feature if you are on the recent patch), more possibilities for map features, and various bugfixes (no more invisible models upon loading saves).
You don't need to remove 1.31 (and maybe older versions like 1.26), but be sure to backup that 1.31 game file, and that your Battle.net doesn't let you update your existing 1.31 installation.