Thank you for your question.
The Lease is a contract entered into between you and the Landlord. I note the provision regarding repairs.
The Landlord is entitled to have his property returned to him in the condition it was let to you, save for any normal amounts of wear and tear. In those circumstances, if repairs need to be carried out then you and the Landlord should seek to agree what works need to be done. This is the first and most important step.
The terms of the Lease make those repairs your responsibility. As such, and once a list of repairs has been agreed, you are entitled to obtain quotes and have them carried out at your own cost. Alternatively, you may be competent to carry out the works yourself in which case you are entitled to do that, provided that the works are carried out to the same standard that a professional tradesman would.
From what you tell me of the lease terms, there is no obligation for you to agree to the use of a handyman in the way suggested by your Landlord.
The most important thing is to agree the list of repairs needed, if any. That is often the stumbling block. You may find that once these are agreed the Landlord's handyman is able to provide a competitive quote in any case.
In short, the Landlord is entitled to have his property returned in the same condition it was let to you. There are a number of ways to arrive at that position and this is a matter for you to discuss with the Landlord. An agreed list of repairs is vital though, so that both parties know exactly where they stand.
I hope this reply is of assistance. Please don't forget to rate my answer so that I can close off your question.