Hmm. "next combat ship?", the Cobra Mk III is not really a combat ship, but a multipurpose ship.
You could step back to the Viper III - a real combat ship - but you won't be able to reuse your modules, you won't get better hardpoints, and you won't get more utilities. So why? Because as a combat ship it is a step up from a Cobra.
You could spend more on the Viper IV - better hull & shield, can reuse more modules, still no better utilities. And it is just a combat ship.
You could stick with the Cobra. You can win the game in a Cobra - with skill - it is that good. I certainly wouldn't sell it. But you do need to pilot well as it is never that strong in shields. Utilities are seriously over-rated for people who want insurance and basically cannot avoid getting shot...
But if you want something "like the Cobra", then the next step up is the Asp Explorer. It is better in many ways - but ultimately it steers as if slightly drunk, and has a hull far too easy to target. It's not really a pure combat ship - but then - neither is the Cobra!! Re-use modules? Yes. More utility? Yes. More hardpoints? Yes.
If you really want a combat ship: Imperial Courier has great shields, can fit an Enhanced Performance Drive, has more utilities, looks great. But it is not really multipurpose. A trivial amount of Imperial Grind is required to get one. Definitely fun.
But given you kitted out the Cobra Mk III for combat, and you don't want a Vulture - the one ship you might really consider is the Diamondback Explorer. You can reuse modules, you will get more utility and more shield + you can afford slots for shield boosters, you will get an amazing FSD jump range, and kitted out right, it'll do combat.