That really is the simplest and cleanest way to do it.
I think it could work to allow your pact blade to be any melee weapon and the damage is 1d10 or the original damage, if it is higher. Then let the warlock attack with their casting stat only if the weapon has finesse or light. That way a warlock could use a heavy two handed weapon but to do so they need to invest in strength. I like the idea of using your casting stat for attacks, but I am kind of hesitant to let them use heavy weapons with it.
Pact of the Blade should probably also allow bladelocks to take warrior feats like rangers and paladins can. When playing around building a bladelock it is pretty frustrating that you can't take any of the good weapon feats without multiclassing. At the very least there should be an invocation that lets you take a warrior feat.
It is a nice way to go about it. I've done similar and it works nicely.
That said... its worth talking about the fighting styles. Like... its not worth taking Fighting Styles or the Weapon Mastery feats, as they don't raise your casting stat. That said? Adding in a Fighting Style as part of the Blade Pact cantrip? That could help bridge the gap in power between using EB and a blade. On the other hand, would we see FS other than Duelist or Defensive taken?
Like... the single best weapon for Pact Weapon options given all the restrictions (assuming no FS/WM, multiclassing or feats) is the trident (d8, thrown, versatile) - same base damage as longsword, plus ranged option. You can't take Heavy, Finesse and Light are meaningless, which realistically leaves Thrown, Reach and Versatile as proprieties you would want on a melee weapon, and it must be melee. With the TWF/Heavy/melee weapon restrictions in place, you can't realistically use the Archery, Protection (no shield), or Two Weapon Fighting Styles with a base warlock. That leaves Great Weapon Fighting, Defensive and Duelist as the only current options, and trident is still best weapon for all possible weapons currently available for these FS. GWF is kinda bad for trident (0.8 avg dmg boost). Duelist can't be used with Versatile it seems, so its effective +1 damage boost. Those are your options for fighting style: +1AC, +1dmg, +0.8dmg.
We could add Weapon Mastery, which would definitely make more than a few more meaningful weapon options. And Pally/Ranger seem like they're getting them. Now, I'm opposed to this on general principle - let the actual Warrior group keep something nice for themselves. Paladins and Rangers should not keep taking the things that make Fighters mechanically distinct; plus, if the paladin really wanted to deal more damage or Topple someone... they literally have smite spells that do that already. And if I'm opposed to Pally/Ranger, I'm going to oppose every other non-martial as well - spells for extra control are a thing after all. But lets put aside my personal objections and pretend that you get a Weapon Mastery for use with your pact blade automatically.
Mastery Properties include Cleave, Flex, Graze, Nick, Push, Sap, Slow, Topple and Vex. Now, given the Heavy, Light restrictions, that immediately eliminates Cleave, Graze and Nick from consideration. Push and Slow (and pull, currently not a WM option) are curiously already invocations you can put on E.B. Flex is really only good on someone with a shield (or maybe with TWFing feats? but not warlock) which the warlock doesn't get by default; given the rules, I'm not convinced that warlocks can't swap between using a trident two handed and one handed plus a focus at whim. That leaves Sap, Topple, and Vex as something -new- to add on.
Anyways, that effectively adds Flail/Morningstar (sap), Rapier (vex), whip (slow) or greatclub (push) as possible weapons if you really want those Masteries. Trident, once again showing its superior ability as a weapon, has Topple. I can't help but feel Topple is superior to Sap, Slow and Vex combined, though with a size restriction. Which makes me feel that the Trident is going to be the weapon of choice for pretty much every Pact Weapon, with a potential great club user for those that want a melee Repelling Blast.
If both the presence and absence of Fighting Styles and Weapon Masteries is pushing the Blade Pact towards the same weapon over and over... that defeats the purpose of adding FS and WM. Might as well just go for a straight damage boost in other ways that are more thematically appropriate.
In terms of other weapon feats... there's Charger, Great Weapon Master, Polearm Master, Sentinel, Sharpshooter, Shield Master, Skulker. It should be noted that all these increase Dex or Str, and not the mental stats that Pact Weapon uses, which lowers their appeal immensely. PAM and SS flat out require restricted weapons. GWM has one feature that you could use (cleave on crit, death), but not the attribute or other ability, which makes it really unappealing. Shield Master requires a feat or MC to get shield first; viable if Lightly Armored survives, but I'm doubtful. Even if you did, Shield Bash is Strength based, a dump stat for warlocks. Skulker... I can't see it being used by anyone without Cunning Action. Charger and Sentinel both work (if you don't mind the off-attribute). Charger is kind of nice when combined with greatclub's Push.
Its kind of ironic, in a way. Hexblade was a fix for Pact Blade, and used CHA to attack to fix some of the MAD issues. Now? We can run Hex/Armor of Agathys and any other spells that don't need CHA. Lifedrinker no longer needs CHA. Using a spellcasting stat means that we don't benefit from a large part of weapon mastery feats or cause or main stat to lag behind, and renders most weapon options meaningless.
We've come full circle.
