It is possible to catch a squirrel in a medium sized humane trap baited with nuts, fruit or peanut butter. However, there are problems if the intention is to either relocate the squirrel or humanely dispatch it. Some states forbid killing game animals without a permit. Others forbid relocating wild or “game” animals without a permit. Also, relocating a squirrel creates havoc where it is released.
The average gray squirrel territory is approximately 2.4 acres. Introducing a new squirrel into an area where there is already a precarious balance of squirrels and food supply upsets the system there. Resident squirrels are stressed, increasing the possibility of disease and starvation. Furthermore, a transplanted squirrel, may return if it is not relocated far enough away. Gray squirrels have traveled as far as two miles to get "home" again.
Humane traps are preferable to leg hold traps which cause suffering of squirrels or local pets which might become trapped. However, a trap such as HavAHartä is only a humane way of catching a wild animal. It does not offer any help in the disposition of that animal. The trapped animal becomes your responsibility. If you are not comfortable with killing it, perhaps you should use an alternative method to deal with the problem such as a professional animal control service.