Whaling tours or vacation packages in the West?

No, there's no way you will be able to do it. In order to hunt in Norway you need a license from the Government:

Norwegian Whaling is subject to strict and detailed regulations concerning all aspects of the whaling activities. There are rules for hunting seasons, quotas, equipment and monitoring. The permission to go whaling is given on an annual basis, and there are certain requirements that must be met in order to get a licence.

One of the most important conditions is the unconditional requirement of having passed the obligatory course for licence holders and gunners. The training courses are mandatory and arranged by the Directorate of Fisheries.

Each year prior to the beginning of each hunting season, the hunters are required to pass obligatory shooting tests, both with rifle and harpoon guns

So they won't let tourists tag along and start blasting away with the harpoons.

As a cultural point please note that in Europe the majority of people find whale hunting barbaric. It would be considered offensive to even ask about it. Even in the parts of Norway and Iceland where they do this sort of hunting, asking to take part would be a very strange request. It would be a bit like a tourist in America turning up at the docks wanting to go out on a commercial trawler.

Generally, whaling on a commercial level is frowned upon, and mostly banned by 88 member states of the International Whaling Commission. There is a whale sanctuary in the Southern Ocean, and even when Japan or South Korea takes some whales for 'scientific' purposes, it's widely condemned.

However, even Greenpeace, one of the staunchest supporters of anti-whaling movements, was the first to congratulate an Inuit group recently when they did some traditional whaling again.

Indeed, since 1991, the Inuit have been allowed to hunt under a strict quota.

So while generally you're unlikely to find legal, publicized hunting trips, if you could - bonding with or contacting an Inuit group and asking to go along with them on one of their traditional hunts may give you an appreciation for their culture, without adding unnecessarily to the death count of whales worldwide.

Among members of the International Whaling Commision, whaling is only allowed for "scientific research" (*cough* *cough*) and on a small and strictly limited scale by certain indigenous populations (see the schedule to the International Convention on the Regulation of Whaling, most recently updated in 2014). Some whaling countries are not members of the IWC and undertake whaling commercially, under government regulation.

Among IWC members, hunting for sport is not a legal activity, since it is not permitted by the Convention; among non-members, I doubt that sport-hunting is permitted and, in any case, the quota will have been allocated to commercial hunters. For example, Iceland's annual quota is only one or two hundred whales (Wikipedia): I'd be very surprised if they "gave" one of those whales to a sport-hunter.

And, no, you can't catch and release with a harpoon. It makes an explosion and a big hole.

I finally found an expedition company with a Sami (Native lapland) adventure in Norway that will offer tourist the chance to hunt whales, herd reindeer, go sledding and spend the night in a Sami lavuu.

I e-mailed them (and about 10 other places) to get more info and confirm.

Now my remaining research question is, is there any other company that offers this cheaper (?!).

The price is about $13,000 for 14 people and it's not until next year. My group size is also not that big. We are 2 people and maybe 2 friends would come along, but we'd have to rely on their company to match us with at least 10 other people.