I get what you are going for but at that point you may as well just have it work like cowboy's 3 hits and have it be a string of swings in one attack. Or make this a rekka character.
Viewing post in Character Concept: Fencer
Eh. The fencer is more of a focus on sword play and tagging than anything. Also, making the pokes their own attack means you will have to SKILLFULLY predict whether you can tag people, rather than just clicking 'flurry' and seeing if your final strike will land before the opponent recovers. I/E You'll need to measure it out yourself rather than seeing a combo play out, and if you overstep it, that's your misplay.
This also lets you choose how hard you want to go with the flurry. Maybe you don't even use a finisher and just back out, maybe you poke away into a riposte to catch somebody who thinks your guard is down. Once you begin a combo on cowboy, you're locked into a combo, but it doesn't matter because the only way out is usually a burst or block all the hits since it carries the opponent. This is a bit more freedom of action at the cost of not flinching enemies and lower damage per attack.