I think it'd be a lot better to go with one of three alternatives...
1. Devices: When you'd normally get the ability to use an HM outside battle, you'd instead get a device that does the job for you. This eliminates that feel of venturing the world with the help of your Pokemon, but from a gameplay perspective, it's the most practical option.
2. All Pokemon get a fifth move slot called a "Utility Slot", exclusively reserved for moves that can be used outside of battle. The Utility move could NOT be used in battle. This means you can have up to six HM's at a time without hurting your Mons' moveset at all, but it limits your team options due to each one only being able to have ONE without messing up their moveset, often meaning you need an HM slave anyhow.
3. All moves -similar- to the HM's carry the same out-of-battle capability. For example... Slash, Night Slash, Guillotine, Psycho Cut, Fury Cutter, etc would all be able to function -exactly- like Cut once you get a certain badge. This is personally my favorite option. It allows tons of options, doesn't limit your team much (if at all), and means things like Cut can become ordinary 'early level' moves like Pound and Tackle.