I always got the impression that not all smugglers worked for one side or the other. Your character just happened to be one of the smugglers that chose a side, and that side was the Republic.

Bounty Hunter may be a little more questionable on that presumption. My impression as that the republic frowned on bounty hunting, so hunters naturally sided with the empire.

Bounty Hunters generally turn to the side that pays the best and, dependant on the area, might actually be legally contracted to carry out said work (though some of their methods might not be.). No reason either could work for both though.

Thanks again for the discussion folks

Out on the edge, it isn't the Empire that you have to watch out for, so much as the Hutts or other crime cartels. Sure, the Empire can hassle you...inspections, regulations, the whole bureaucratic nightmare. Hutts don't do that. If a Hutt wants you dead, they'll have a list of favorite bounty hunters to send. What was it that Greedo said about 'a bounty so high, you won't be able to go near a civilized system', or something to that effect? Yup.
And even if the PC's get tossed in the pokey by the Empire, whos to say that someone on the same ship, or in the same spaceport/brig/jail/etc. isn't on a Hutts payroll, or is otherwise being influenced by a Hutt.
The Empire can lock you up...maybe execute you. Hutts just blow up your ship, then have lunch. When you have a Hutt who has made up their mind that you have to die right now, you really don't have time to get into the whole Empire and Rebellion thing.

The Empire has no problem blowing up entire planets for show... I doubt they can't find a way to make someone "disappear".

I don't want my campaign to morph into Age of Rebellion - another member of our group is already running an AoR campaign!

To keep things separate, I run the Empire as just one of many possible antagonists in the campaign, rather than the primary villain. My players have found themselves in the employ of the Hutts, Black Sun and private clients, and occasionally they cross swords with the Empire if their current mission means that their goals clash. The Rebellion are just one more faction who could be a potential employee/threat.

For example: an upcoming adventure I am writing - "Family TIEs" - will see the group hired to steal a prototype TIE fighter by a mid-level member of Black Sun - mainly so that the criminals can make sure they know how to outrun/avoid this new type of interceptor should they need to. However the Rebellion are after it too - so the players have to choose their loyalties. They could end up being in direct conflict with the Rebellion, or could double-cross Black Sun...

Give them a few "friendly" imperial contacts as well, the corrupt moff/govener that's pushing to sell product in a time where they regulate it. The catch? Their influence is usually limited and they have to at least show an interest in keeping the law, thus hiring of smugglers could both be a well paying risk and threat. Is he double crossing? Or is it just an imperial petrol vessel that happened to be there.

Or is it just an imperial petrol vessel that happened to be there.

I would go with an Imperial Hybrid Vessel, petrol vessels are terrible for the environment