Yeah, you're actually fine mixing them at level 12. Oblivion's not like Skyrim where you're locked into a skill tree forever—you can totally swap weapons and level both skills without gimping yourself, especially on Normal.
That said, the real difference is that Blade and Blunt perks are completely separate. So if you commit hard to one, you get access to perks the other doesn't have. Blunt has some solid armor-ignoring stuff if I'm remembering right, while Blade gets more crit damage bonuses. But honestly? At your level, it barely matters. You're not hitting the high-tier perks yet anyway.
The thing Oblivion does that Skyrim doesn't is let you actually use multiple weapon types without penalty. Your skills level independently, so a mace one minute and a sword the next won't "waste" anything. You're not spreading yourself thin so much as just... not specializing yet. Which is totally viable.
If you want my take: pick whichever feels better to you right now, and don't stress about it. By level 25-30, if you want to focus on one, you can. Or just keep using both—Oblivion's way more forgiving about build flexibility than people remember. The real trap is trying to be good at everything (all skills maxed), but two weapon types? That's nothing.
What difficulty are you actually playing on, or just Normal?