You can insulate your walls without tearing them apart.
There is a foam insulation that has always been popular in Europe, but got a black eye when they tried to market it in North America. Basically, they drill a hole in your exterior wall and pump in a foam that expands and fills the cavity between the wall studs. Once the foam fills the cavity and stops expanding, it releases formaldehyde gas for several days as it solidifies and cures. It's a highly effective product both to stop drafts and to provide a very R value in terms of insulation.
But it got a bad rap when there was a scare back in the 70's about people getting sick from the stuff. There were all kinds of claims made that the formaldehyde continued to be released from the foam for years, and that this was making people dizzy, confused, lethargic and unable to work, it supposedly gave people headaches, made them cough, sneeze, puke, have insomnia, etc., you name it, someone claimed it.
But, when they launched a class action law suit to sue the manufacturer of the stuff along with the Government of Canada for encouraging people to insulate their houses with it, they couldn't find any houses that had significant levels of formaldehyde in the indoor air. In fact they found that houses with a new carpets had higher levels of formaldehyde in their indoor air than houses with UFFI foam in their walls. So, the law suit fizzled out, but UFFI foam has never made a "come back" in North America because people associate the name with "sick house" syndrome.
It's called "urea formaldehyde foam insulation", or "UFFI" for short, and in Europe it's considered one of the best ways to insulate a house. In Europe, there were never any claims made of people getting sick from it, and so it's never come under attack there like it did in North America.
Maybe Google UFFI and you can read about the history of the stuff in Europe and North America and decide for yourself if it warrants further investigation. You might find someone selling an "DIY UFFI insulation kit" in Europe.