The heat gun they use is called reflow station, rework station or hot air station. For these kind of components it is inevitable to use one of those. Nowadays they are not that expensive, you can get one at about $60. Not the best quality for sure, but will do its work.
HalloweenBob know if the investment in all the equipment needed to do the job is justified for me, since I won't be making more than a few sets of these as far as I know.
Only you can tell. If you do some occasional soldering as a hobby then having a rework station on your lab can be helpful for many tasks. An alternative might be getting in touch with a local fablab or hackerspace. Those kind of places usually have the equipment you need and offer ways for the public to use it. They are also a good place to meet experienced people who might be able to help you, or even commission them the job (but it is normally not a cheap one).
Since you got this far I encourage you to try to it by yourself. I know it seems spooky before you start, but with some perseverance it is not an impossible task.
A --perhaps-- cheaper alternative to the reflow station is to make yourself a reflow oven hacking an old toaster one. Search for
diy reflow oven and you will find many examples and guides.
Or.. another even cheaper alternative is to use an electric hot plate. I never tried that one myself, but many people argue that it is a really good alternative. Search for
hot plate reflow, or something like that.