Thanks for your question. I will try to help.
Unless the right of way is limited to a access at a particular time or subject to them giving notice then you are probably going to have to give them a key.
The right is a legal easement which gives the person the legal right to access the property in accordance with the wording. They may practically only use it once a month but if the wording is not limited to this or to a requirement for them to give notice then you do not have any legal argument to not give them a key.
If they are not satisfied with not having a key, then I would give them one basically. I appreciate that security might be an issue for you, but when you purchased the property with the right of way you effectively accepted a certain limitation on absolute security.
Ultimately, if you do not provide them with a key then they could apply to court for an order that a key is delivered up to them by you and probably also claim their costs for doing so from you. This is of course if they were minded/bothered to actually apply to court, so you may wish to test their resolve but ultimately accepting that if they appear sufficiently motivated to make an application then to deliver a key before proceedings are issued.
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