I originally thought this as well. Wifi should not make for a slower player. From an in-between perspective, if you will, I can honestly say Wifi has made me think much more about what I do, as well as bettering my reaction time tremendously. It's really hard to cope with at times, as lag can highly interfere, but it should not lessen any aspect of your play. It takes personal experience, but Wifi can make you faster, actually. Not as fast as you would be playing straight-offline, but you'll find that it's much easier to play sometimes when you're opponent isn't right next to you; if you're like me, it's a tad pressuring, and I can't keep my cool and make dumb moves. Online, I'm able to pay attention to what my opponent is doing more carefully and precise than offline.
tl;dr: Wifi should not be making you play slower, especially if your connection is prime choice with the people you're playing. The transition from online to offline in even timely intervals can seem really really drastic. Just get used to it, and you'll be able to tell the difference between the two when need be. I don't think I would have gotten anywhere in my competitive career without Wifi.
Feel free to ask anything else if you have more questions.