You want the shrouds attached while stepping/unstepping the mast. That will give you some (but not total) control of the side-to-side position of the mast and especially if you are alone it then gives definite side to side control once mast is vertical. You may need to have the turnbuckles loosened slightly to provide some play, but you really need to have them attached while stepping/unstepping.
Here is the Mast stepping procedure as listed in the 222 Owners Manual: (There may be slight differences based on whether you have the Z-Spar Mast or the Dwyer?)
Stepping the Mast:
CAUTION: BEFORE STEPPING THE MAST, BE SURE THAT THERE ARE NO OVERHEAD WIRES OR TREE BRANCHES. ALSO CHECK THAT THERE ARE NO OVERHEAD OBSTACLES BETWEEN RIGGING AREA AND LAUNCHING AREA.
We recommend that you have assistance in stepping the mast. The mast should have the slot facing aft when stepped, or down when horizontal. Open the turnbuckles at ends of stays to half-open position. Then attach the Backstay to the stern chainplate, with clevis pin and cotter ring (See Fig. 4) and proceed to attach Sidestays, both uppers and lowers, to the side chainplates. The lower Sidestays that go to the mast tangs located just below the spreader bases are attached to the forward part of the chainplates, while the upper stays that go over the spreaders attach to the aft part of the chainplates. (See Fig. 2) Do not attach the Forestay to the bow fitting yet. A tabernacle is provided on the cabin top of the O’DAY 222 for ease in mast stepping. With the mast in a horizontal position and the main hatch closed, insert the aft mast base tabernacle pin and cotter ring into tabernacle (See Fig. 3). Next push up and forward on the mast until the mast is in a vertical position; it helps if one person pushes the mast up while a second assists by standing on the foredeck and pulling in the forestay. Now with one person holding the mast vertical, the other can attach the forestay to the stem fitting near the bow (use forward hole) with a clevis pin and cotter ring. Next, insert forward pin in the mast tabernacle and secure it with the cotter ring. After all stays are securely attached and the tabernacle pins are in, take the slack out of the rigging and tighten. Try to ensure even pressure upon the mast step/tabernacle pins in a fore & aft direction. With the mast so positioned, the Forestay, Backstay, and two upper Sidestays should he tightened no more than hand tight. The two lower Sidestays should be just taut, not hand tight.
CAUTION: IT IS VERY IMPORTANT THAT YOU DO NOT TIGHTEN THE STAYS TOO MUCH, AS THIS CAN CAUSE DAMAGE TO THE HULL. BE SURE ALL LOCK NUTS ARE SECURELY TIGHTENED BY PLIERS OR A WRENCH AND THEN TAPED TO PREVENT LOOSENING.
After the stays have been adjusted, insert the cotter pins in the turnbuckle studs. (See fig. 2) Bend the cotter pins over and securely tape the cotter pins to prevent them from catching on anything.
Normally, on a trailered boat, only the forestay needs to be unhooked to lower the mast; thus the other standing rigging can be left adjusted for the season. The forestay will need to be loosened each time to unstep the mast, and then retighten after stepping the mast.
I'm not totally familiar with the 222 chainplate setup, but on other similar boats (CAL 21 was one) a good tip was before stepping the mast, tape the 2 turnbuckle toggles together so they remain vertical while raising the mast, one thing that often caused the turnbuckles to get bent was when one or both toggles flopped over to one side preventing them from properly pivoting. Hard to really put into words.........wish I had a good picture showing what I'm describing.
The problems that Brian S talks about with the backstay are common to many sailboats, the backstay on our old CAL 21 would get hooked on the mainsheet cleat and prevent the mast from being able to fully go up.... and it was difficult if not impossible to fix that without a 3rd person (typical routine was one person pulling on forestay and the other walking mast up from aft.....). We rarely unstopped/stepped mast ourselves, but I remember always needing to watch that backstay!
One other good tip, if possible, try to point the boat with the bow facing downwind while stepping mast, that was any wind force will tend to help (OK, very little, but...!) rather than hurt and more importantly will not tend to blow the mast over to one side or the other.