For Slave I? I would tend to think something along the lines of a Wolf, Lasher, or Vigilence. Slave I's a modified police ship, not a full-fledged warship, and the Vigilence, as a purpose-built patrol ship, comes fairly close to that profile. The medium missile and medium energy mount don't really align that well with what we see of Slave I's armament, but that's not that much of an issue in my opinion. My second pick would be the Lasher, as it's a somewhat outdated warship that probably gets used for system patrol on a regular basis. Third place, in my opinion, goes to the Wolf. A Tempest might work, too, although it's not really the kind of ship you'd be wasting on system patrol duty, which was an intended role for the Firespray.
I personally do not feel that the Hyperion fits the description. It's too overtly a heavily-armed top-of-the-line combat frigate, and its cargo capacity is too low to allow it to be employed as a lone ship with any real effectiveness at any significant distance from a supply point. Its cargo holds enough supplies for a ~33 day round trip, but if you deploy it even once it'll demand half again what it can hold to recover to its pre-battle state even if it doesn't take damage. It is by far the most expensive frigate to deploy, costing 3 times more supplies to recover than the runners-up (the Tempest and the Omen, which each take 5 supplies to recover) before including any repair costs, and it's also the only frigate in the game, aside from the Ox, that cannot carry enough cargo to at least fully recover once. Even the Tempest and the Omen can carry enough supplies to fully recover from 6 deployments (neglecting crew costs, hull repairs, and non-recovery periods); the Hyperion can't even fully recover once. Worse, it takes two to four times longer for the Hyperion to recover than any of the other combat frigates require. This seems like an incredibly flawed vessel to use as a lone ship, even if you're only intending to use it for intermittent low-intensity combat. I could see a wealthy government using these, or perhaps a corporation trying to show off their wealth instead of their good sense, but without the backing of those kinds of resources and without available backup vessels (both for carrying the supplies to make any sort of extended expedition practical, and for providing cover should there be need of fighting at a time when the Hyperion is recovering) it's just not at all a good ship to use. To some extent, I'd even say that its firepower is to its detriment, if bounty hunting in Starsector includes the 'bring the target in alive' kind of deal that Fett was employed to handle in Empire Strikes Back, though this can be alleviated somewhat through weapon choice or the intimidation factor of having a ship bearing down on you loaded with antimatter blasters and atropos torpedoes. I'd also argue that the Hyperion is too obviously a top of the line combat frigate to be a good analog for Slave I, which to casual inspection would appear to have a lighter armament than the Millenium Falcon has, probably even after accounting for the slight difference in size. Slave I can probably pass for a civilian vessel armed within legal limits in most or all of the same areas that the Falcon can. The Hyperion isn't going to pass as anything but a heavily-armed mercenary, corporate, or governmental warship anywhere it goes unless you load it with annihilator rockets and PD lasers.
