Why should you demolish that old building, it is doing no harm to anyone? There are many reasons why you should do something about old buildings that have fallen into disrepair.
Is it dangerous? Could a child playing there be hurt or killed by falling masonry?
Is it insured? Would you be personally liable for any injuries that happened, or would the insurance company pay? Are you sure the policy covers derelict buildings in a dangerous condition? Very few do.
It is an eyesore.
You have ideas for replacing it
How do you go about getting rid of it?
Sure, a handyman can take apart an old building stone by stone, timber by timber. Are you going to do it yourself? Are you positive that you can work out the order of safe dismantling?
Have you someone to work alongside you, because this kind of work should never be done alone? Would you do the job by hand or hire machinery to help?
If you hire an odd job man to do it, he is unlikely to have any special training, and is likely to be a hazard to himself, you and the general public. Unless he has insurance, you may be liable for any injuries during the demolition...