Removing the airbox is not difficult, I'd recommend pulling it. This will give you the chance to clean it out, the inside can get a bit dirty over time.
To remove it, you must first remove the seat, side fairings and fuel tank, the last of which can be removed with the upper fairing still in place, but you must remove the screw on either side of the fairing which attaches it to the tank. Once those are out, the fairing is flexible enough to allow removal of the tank.
Next, there is a bracket above the airbox, held in place by 4 m6 bolts with 10mm heads and is what the back end of the fuel tank bolts to, which must be removed.
Next, remove the side covers from the airbox. It will be 4 phillips head screws per side.
Now the airbox can be lifted out vertically. Be aware of the rubber intake hose on the right side (it will be visible once the side cover is off), it likes to get in the way, you may want to pop it out to ease removal.
A note on reinstalling the airbox. The rubber boots which you are replacing have springs which help hold them onto the carburetors. Roll these springs back off the groove they sit in back to the narrowest point on the boots in the middle. This makes it much easier to get them to slip onto the carburetors. Once everything is set in place, roll the springs back into their groves on the boot around the carbs. If you've got long fingers like me, this can be done without tools. If not, a flathead screwdriver will be helpful.