Up for Heir by Stella Starling

A playboy heir needs: a man to marry, right now.
After spending half his life dodging his duty to the crown, the rebel heir to the Rosavian throne has been told in no uncertain terms that it’s time to settle down. Prince Leopold has one month and a vetted list of suitable princesses, and he will announce his engagement during Rosavia’s Royal Ball. But Leo’s got his own ideas about what really suits him…
Royal Librarian Edvin Blom is good at not attracting attention. Shy and self-conscious of his stutter, he’s used to being overlooked and more than happy to stay in the background. At least, until the Crown Prince with a wild reputation shows up at the library’s new opening and decides to flirt with Edvin’s sister…
Edvin isn’t at all what Leo thought he wanted, but turns out to be everything he can’t stay away from. Edvin’s been burned by falling for someone out of his league before, though. And believing that Leo has really fallen for him? While Edvin’s drowning in his own doubts and insecurities, that might prove impossible… unless love gives them both a reason to come up for air.