It’s a half-hour project, 25 minutes of which is spent cutting off the ends of of the plumbing supply line and patiently teasing out the plastic tubing. You can also buy those supply lines ready-made (I was able to talk a Home Depot guy into cutting the ends off for me after I bought the hose, which helped a lot). Assuming you know how to wrap teflon tape and assemble threaded parts, you should be fine.
Thanks for the help everybody. The hose washers, plus a longer nipple, ended up doing the trick. I let it sit with 2 gallons of water for 45 minutes or so without even a hint of dampness.