I'd use a Luminex panel. They have the widest range of multiplex panels for detection of cytokines, and if you need to, you can make your own, or have them make it using materials you specify
There's a number of ELISA kits for cytokines. But they aren't as broad. You can get multiples of them though, and if you just have a small number of samples, that may be cheaper. But for semen studies, you may have some trouble getting a large enough sample. Which is why I would use Luminex (or some form of cytokine bead array system). Luminex beads have been used to measure cytokines extracted from a fraction of a fetal blood spot, decades later. You won't have a problem with having enough sample.