A LiPo reaching a higher voltage than stated on the LiPo is quite normal and is not actually "over voltage." Generally, when talking about a LiPo battery cell, 3.7v is mentioned because that is the nominal voltage of the cells. However, when fully charged, a LiPo cell should reach 4.2v. So for a 4s LiPo, 14.8v would be considered the nominal voltage but when fully charged, a 4s LiPo can reach 16.8v.
Seeing as you have a 15v limit, there are a few options. Firstly, as you mentioned, you could discharge the 4S LiPo to 15v and this should work just fine, although you would be losing a significant part of the battery's capacity. Alternatively you could get a 3s LiPo (if that is sufficient voltage) because a 3s LiPo will not go above 15v. And lastly, if this is an option for your project, you could use a 15v power supply to deliver steady, consistent power.