Can anyone advise whether I should be using TS (unbalanced?) or TRS (balanced?) cables from an RNP to a Delta 44 (or whether it matters)?
how long are the cable runs?
Short (~20' or less)= either will be just fine.
Unblanced cables are more likely to pick up electrical noise if run by power sources.
Balanced cables (Differential)reject common mode noise and can be run for longer distances.
TS leads will work in this case, but for running from a balanced output to a balanced input you should really use balanced (TRS) cables.
However, your main concern here is not the balancing but the signal levels. The RNP will drive at +28dBu (balanced or unbalanced), where the Delta 44 clips at +14dBu. This means you are in great danger of overloading the Delta. I would consider getting a pair of switchable line-level attenuators that have a 15dB attenuation setting. These are probably only available with XLR I/O, so you would need a complementary pair of XLR-TRS cables. Avoid attenuators that are designed for microphone levels only. If you are handy with a soldering iron, you can make a 15dB attenuator using a pair of 4K7 resistors and a 2K resistor, the assembly housed in the jack plug or as a lump in the cord.