I would get some CO2 and just squirt some into the carboy and leave it alone. You could use one of the pocket chargers they make for serving corny kegs without any other way to get CO2 into it. If you're set up for kegging, then just use some CO2 from your tank/bottle. You don't need much here, just enough to blanket the mead.
BTW, the above except about fermenting and producing CO2 is all well and good. BUT, I always wait to rack (the first time) until the batch is 100% finished fermenting. I rack depending on the yeast and how it's actually been doing. Sometimes that's a month after pitching, sometimes it's 3-4 months after pitching. It all depends on the yeast.
Also, I wouldn't rack again until at least a month has gone by. Between now and then, get a vessel that's closer to the size needed. I would also put some CO2 into the vessel the mead is going into, and rack to under that.
Personally, I'm using adapted sanke kegs for all my fermentations. That's for beer, mead, skeeter pee, anything that I pitch yeast into to get alcohol content. With this setup, I simply hit the receiving keg with some CO2, unseal it, install my racking cap (TC cap with a liquid ball lock post and dip tube fitted) and transfer into that from the source vessel (fitted the same). Depending on which racking this is, I'll either use a full length dip tube, or one cut to leave something behind. When the batch is aging, they get fitted with solid TC caps over the sanke valve opening. I then use the gas post (fitted to each vessel) to vent excess CO2 periodically. With this setup, I don't worry about much of anything. When a batch is aging, it can even get kicked over (if someone wants to hurt themselves) and it won't leak out, the vessel won't break, and I don't have to worry about anything unwanted getting into the mead/beer. Since I've long since gotten past the 'need' to see what's going on inside the vessel, not seeing inside doesn't bother me.