You could drop the dry hop pellets through the airlock hole, work fast. I think that's minimally invasive, and may preserve the headspace better than cracking the lid just enough.
You still need to agitate the fermenter as the added dry hops tend to float. A gentle swirling once or twice a day.
After 4 days of dry hopping most if not all dry hops will be on the bottom, with the yeast. To complete settling out, put the bucket is a very cold area, if you have one, for another day, without agitating. Then rack or transfer to a bottling bucket and bottle away. You can tie a fine mesh hop bag around the output of your racking/transfer hose, and lie it flat on the bottom of the bottling bucket, it will trap any hop material that inadvertently got transferred.
Start racking/siphoning from around the center of your bucket, halfway between the bottom and the beer level. Slowly lower it as the beer level drops. Toward the end, tip the bucket toward the siphon/cane (held along the side) to keep the beer well deep. Don't be overly greedy. Use that flow-inverter tippy that comes with your cane/siphon. An extra pair of hands comes in handy, makes the whole bottling process more fun too and faster.
Train ahead of time with a bucket of water.