In this article, we propose a numerical algorithm capable of handling optimal control problems for a class of systems with input-dependent input hydraulic delays. Such delays are often observed in process industries. A careful look at the stationarity conditions allows us to derive an iterative algorithm approaching the solution of this problem by solving a series of simpler auxiliary instances. Interestingly, the algorithm is able to leverage state-of-the-art numerical optimization tools such as IPOPT. The proof of convergence is sketched, highlighting the relevance of the chosen algorithmic structure as a form of gradient descent in a functional space. The practical interest of the algorithm is evidenced on a numerical example, showing the desirable properties of convergence and the numerical efficiency.