Off the top of my head, here's how I'd roll a character like this:
Tag Cowboy and try to stick to revolvers as your main weapon - take Gunslinger and Rapid Reload, in addition to Quick Draw (Quick Draw more for flavor than actual usefulness). General gun related perks for boosting damage, like Center of Mass, are also a must. I would also recommend grabbing Finesse and Better Criticals. Toughness, because it's Eastwood, after all. Also consider getting the Sub-Dermal Implant, since that's a kind of permanent metal breastplate hidden under your poncho.
Gear: Pick up the Sheriff's Hat in Primm ASAP for a cowboy look. For a real challenge, stick to light armor for the whole game: leather armor, various dusters, Joshua Graham's Armor, Daniel's clothes, etc.
Companions: Raul and/or Cass. The others are optional. Make sure you complete Raul's questline so he can rock his vaquero outfit.
As for SPECIAL, I'd recommend making Agility and Luck your highest stats. Aim for at least a 5 in endurance so you can get Toughness. You'll want to get at least 6 strength at some point so you can the Hunting Revolver, That Gun/5.56 mm Pistol, etc. Perception should be at a base of 6 for perks.
Charisma: Let me just begin by saying that I am REALLY not a fan of using Charisma as a dump stat - I find minmaxing in an RPG to be kind of lame. It's totally unrealistic to have a character with 1 charisma but a high speech level, unless you are literally playing as an android like Data or something.*
Now that said, The Man With No Name strikes me as the mysterious, quiet badass - not exactly a used car salesman type or a diplomat. Given that, I think you could shave a few points off Charisma (maybe start with a 4 or even a 3) to reflect this without making your build into some kind of immersion-breaking, non-RPing minmaxing build. Unless, of course, you're into that.
On the other hand, you may want to start with a higher charisma or at least focus on increasing Speech to 70 so you can get the "Terrifying Presence" perk, since being able to effectively intimidate people does seem to be in keeping with the character.
* Sometimes I wish that NV had instituted some way of capping skills based on your SPECIAL stats - so, that for example. a character would need to have at least a 7 in any given attribute to max out the skills associated with it. That would have prevented stupid builds that want you to dump Charisma to 1, but still Tag Speech. Nearly every guide to NV suggests you do this. Drives me crazy.
