A few observations on this dangerous territory.
Some insurance policies exclude liability claims arising out of or in connection with the use of chain saws.
Attempting to contract out of your liability for injuries to the chainsaw merchant and or his son would most likely be problematical.
People may turn up to your property with signs on the sides of their vans declaring that they are "fully insured".
That usually means precisely nothing.
Whose liability is covered, to whom and for what contingencies ?
The "contractors" may have public liability cover that indemnifies them for their liability for an accident but not the householder.
I make precisely the same observation in regard to employers' liability.
Generally, a principal [in this case the home owner] is not vicariously liable for the negligence of an independent contractor.
However if, on the evidence, the chainsaw merchant turns out not to be an independent contractor the home owner may find themselves saddled with the liability for an accident. This could include injuries to members of the public caused by the contractor.
There are a number of other permutations and complications that could arise in this type of situation but I will not go on................
In summary, my firm advice would be to steer clear of this type of casual arrangement as if things go wrong you will find it a very costly experience.
Engage a bona-fide contractor to do what is reasonably regarded as potentially dangerous work.