PC being silly, so apologies if I tread ground covered by others.
First problem is partly semantics - the phrase 'bear defence gun ( sic )' means one thing to the general populace, but something specific for a gun nut.
In the specific sense, it conjours an image of defeating a charging bear at ranges where his halitosis is a major threat
The fabled Guns and Ammo magazine ran an article several years back - to test the ultimate bear stopper. Think they used a 44 magnum Ruger, 45-70 or 444 Marlin lever action and a custom Remington 870 in 12 bore. All arguable for that task, but fairly limited for much else.
By simple laws of physics, anything ballistically big enough to blunt a bear is going to be a hard kicking piece and require some dedication to use effectively. If you are a weapon user rather than enthusiast, there is the real risk that you will not develope sufficient skill/ muscle memory to deploy the piece effectively in the gravest extreme.
It is equally hard to quantify 'general hunting'. For bunny bashing etc a .22 is hard to beat, easy to carry and light weight ammo. But much bigger - certain deer size animals and it is inhumanely underpowered.
Sorry to hear about the shotgun legislation - that is the most general use item you could go for. 12 or 20 bore slug would be a reasonable close range bear medicine. With shot or even a sub calibre insert it would do rabbits on up. A reasonable side by side type would also break neatly in two for transport.
Legal side I do not have much knowledge of travelling - but understand most the rest of the world is relatively easy - compared to when you get back to UK! EU countries should be straight forward with European FA pass.
Shotguns require a certificate - but currently much less hassle than a firearm certificate. Solid slug for a shotgun would however require a firearm certificate to possess in the UK.
Unless you intend to shoot in the uk at all, any heavy calibre firearm is going to be an administrative nightmare. In the UK expanding ammunition is prohibited - with exemption for specific use - like deer stalking. The police will decline you authority to purchase expanding ammunition in the UK for use on big game overseas.
If you have a specific country that you will visit, maybe worth checking law and possibly keeping a suitable weapon in country.
Outwith my experience, but how do these bear pepper spray devices perform? Are they legal in the countries you wish to visit? I would only finally echo previous contributor - firearms aside, best route is a crackjack routine for bear avoidance and conflict de-escalation - even if backed up by a fistful of firepower.
Good luck.