You should really ask the studio how they want it done. I am doing similar jobs for clients and here is my advice on how you should do it.
As long as your audio interface has a Hi-Z or Instrument input you're good.
Radial, one of the reamping pioneers, does recommend using a DI for tracking though:
Start by recording with the industry standard Radial J48 direct box.
This active DI is ideal for Reamping as it will not load down the
pickups and will deliver the true sound of the instrument without
distortion or artifact.
But this is really just a general advice - using a DI will work regardless of wether your audio interface has a Hi-Z / Instrument input or not - a device with a Hi-Z input doesn't "load down" the pickups.
Recording straight into the interface will not introduce additional noise - on the contrary you make the signal path shorter (and the introduction of a balanced additional path span will definitely not remove noise from the initial unbalanced part from guitar to DI). What is extremely important is these points
- Make sure your guitar is turned all the way up
- Use a high quality cable and don't place it on noisy things like power supplies
- Record in 24 bit, >= 44.1 Khz
- VERY IMPORTANT: test the best location for the guitar - there are many electric noise sources (CRT screens, laptops, lights, cell phones, power supplies etc) that will get picked up by the guitar. Put on a heavy distortion plugin temporarily and move around listening for the best location and angle and mark that spot.
Additional info if you are reamping yourself
Reamping using a real reamp box
However if you are reamping out through real amps you will need a reamp box ("reverse DI") and possibly also a volume pedal if your reamp box does not have an attenuation pot. I can recommend the Radial devices, e.g. this one:
Alternative Reamping using a passive DI in reverse
If you find the Radial devices too pricey there is a cheap alternative - get a passive Behringer DI (e.g. DI400P) or a Millenium DI-E and use it in reverse (i.e. Audio Interface -> DI Out, DI In -> Amp). The DI box is very simple - it only contains a transformer, a switch and the connectors - these components doesn't care at all about the "direction" of the signal:
You will need to attenuate the signal after the DI though, since it is too loud to go directly to the amp, and turning down the output digitally will introduce alot of noise. Here is a pic of the Behringer DI400P box and the Millenium DI-E: