Yep that will do the trick nicely - I presume you do mean the air vent at the back of the armrest above the cupholder
Easy to replace - fold down the cupholder and inside there are two torx screws, remove these and they lever the tabs you can see on either side of the cupholder inwards and you will be able to pop out the cupholder. Then get a flat head screwdriver or trim removal tool at the bottom of both sides of the rear plastic part that now only has the vents in it, lever it backwards to unclip the rear trim piece. Once you have the clips at the bottom unclipped (can be a little fiddly) you can remove the whole rear trim bit by lifting it upwards and away from the rest of the armrest.
Once out you will see that the vents are held on with 4 little vertical tubes that have been pushed flat to hold the vent down. Cut the ones that are holding the vent and then you can lift the whole vent out. You will be left with 4 other tubes which you can slide the new vent on to, and then fold down those tubes to keep the vent in place - add superglue for extra hold if wanted
For reference this is what the rear piece of trim looks like removed
Simon