If you don't want LED's all 3 jacks can be simple 2-conductor, and leave out the resistors, and then the switches are SPDT instead.
Ground all the grounds together at one spot: take a ground wire from J1 and a ground wire from J3 (the "shield" terminal) and run them to the "shield" terminal of J2, that's all that's needed.
Yes, the resistors by the LED's are just dropping resistors to supply the proper current/voltage to the LED's.
Personally I'd say, if you're going to this much trouble to make a switching box, go ahead and get the DPDT switches and take a few more minutes to put the LED's in. It's kinda nice to know which side is active--for example I use my bos to switch between acoustic and electric guitars, i've only got a couple of seconds between songs sometimes, things get hectic on stage,and without the LED's I wouldn't know immediately which one was hot.
For the LED's, the one change I'd make: I'd make J2 the 3-conductor jack (instead of J3)...this is always the "common" jack.
edited: I re-read your posts, do I understand that you aren't even going to be doing any switching, you just want a box with 3 jacks in parallel?
Run a ground wire from shield of J1 to shield of J2 and another from shield of J3 to shield of J2. Run the hot wire from tip of J1 to tip of J2 and another from the tip of J3 to tip of J2. You're done. No switches, no LED's, no resistors. 3 jacks, a few short pieces of wire.