I never attach parachute shroud lines directly to the nose cone. If the nose cone passes through any two lines your parachute lines are tangled. I'll add a longer shock cord and tie the cute on about 1/3 the way down (and away) from the nose cone.
Snap Swivels are about 10 for $1.00 pack at WalMart. Save yourself from tangles and be ready to easily switch out a smaller parachute when the winds are up.
The shroud lines on my Big Betty kit were too thick to go through the small eyelet on a snap swivel. I could eventually get all three loops through, but sometimes it's easier just to tie them on the eyelet using some thick rug and button thread.
The outside shroud line loop is tied onto a length of strong thread. Tie the thread to the center point of the shroud line.
The picture shows the third shroud line loop being slid down the strong thread. At the apex of the "bend" you can see the center mark made with a marker.
The third shroud line is tied to the thread. I doubled over the thread through the loops again for strength.
No tangles and the swivel is ready to attach to a loop tied on the shock cord.
This is the same method I used to tie the parachutes to snap swivels on the Estes Saturn V build.
The shroud lines in the reissue kit were also too thick to go through the swivel eyelet.