100BASE-T can run over string (literally; well, saltwater-moistened string, of not too much length), don't worry about it. In particular, anything you do with a smaller connector, is likely to be strictly better than the signal quality from a normal 8P8C connector -- mainly because, if you're choosing your own type and pinout, you can resolve the stupid* 1-2, 3-6 pinning that became standard.
*Various historical reasons, of course, but so it goes; that doesn't absolve it from being poor signaling practice. But still, baud rates are low, it isn't a long enough mismatch to matter.
Any pin header will do; take your pick between size, cost and robustness.
I'm currently somewhat "into" TE's HPI series; the 1.5mm pitch in particular, is easy enough to use but still reasonably high density. It is a bit fragile, not suitable for many insertion cycles, or much tension on the wires (which are thin, 28AWG), but that's fine for internal connections in commercial grade electronics.
Tim