Living in France, I have people pass by every two days offering such services. But you're probably in CH.

Do not underestimate the work of disposing of the wood. A tree of 8m has a huge quantity of wood. Make sure that you include it in the job of the entrepreneur.

It mght be a good idea to go see your local mairie about this. You may need a permit to fell trees. It may depend on if they were there when  you arrived, or if you planted them yourself, where they are situated and what species they are.

Could be the Maire might arrange for someone from the local forestery commision to come  take a look.

if you are living in rented accomodation you will need the permision of the owner of the building,

If you can fell  the trees, make sure you are well insured for any damages that may occur whilst this takes place. In some occasions a felling company may have suitable insurance themselves and in some circumstances may even be interested to buy the wood from you, which may offset the cost, which could be quite high dependant on the circunstances..

This old thread from another expat website may be useful.

https://www.englishforum.ch/housing-general/312465-cutting-down-trees.html

Hello, 

We recently had removed a really big tree from our place. You need to get authorisation from your local mairie.  We found a Swiss company who helped us with this process including disposal of the wood. Let me know if you would like the détails of this company.