There is one caveat to running a science ship with a non-science character.
To have high effectiveness, you're going to need to spec into several fairly expensive science skills. In order to avoid having to pay for this you're going to have to do it relatively early on, too.
This is because all the science skills most tacs and engineers ignore (e.g. subspace decompiler) are necessary to leverage the nastier science skills, and on a science ship you're going to have those out the wazoo.
Cruisers and escorts don't really suffer from this so much, since most of their skills are fairly applicable to one another - both can benefit from extra weapons power, for instance.
You also needs a very clear idea of what Science powers you will be using with your Captain.
Subspace Decompiler doesn't need to be skilled if you aren't using VM's or Disables with long durations. Graviton Generators doesn't need to be skills if you're going to use Tractor Beam Repulsors.
The only two [Offensive] Science Skills most any Tactical Captain will pretty much always put ranks into are Particle Generators and Flow Capacitors and Tactical Captain skills increase the damage and Drain Magnitude of quite a few Science powers.