You might propose a compromise, such as a lock box. That way, your key isn't floating around. And, even if your lease is silent on the point, you might reasonably request some sort of notice (such as 2 hours, or 4 hours or whatever) prior to showing. And you can explain politely to your landlord that this will work to his advantage as well as yours; it'll allow you to make sure that your unit is presentable.
But, first, read the lease. Then, if necessary, check with a lawyer.
Hope that helps.