Don't it feel good? ;)
Touch up on the coti? Now you're really getting into preferences and experience. Clearly your razor is shave ready as is without the toe issue. If you take that edge to a coti, even on water, especially if you've not honed before, I'd argue it will get duller. That being said, most fully stropped coti-edges I've gotten are duller than what I can get from a Croxified(tm) edge. However, the coti edge can clearly still be shave-ready and can be smoother and more comfortable than the sharper CrOx edge. So duller (shall we say, "less keen") isn't necessarily worse. However, if you are new to it, you might accidentally reduce keenness to the point it isn't shave ready anymore, even on water. If so, you might bring it back with CrOx. Or if you lose keenness too much on water due to lack of practice, go ahead and crank up the slurry and just go whole hog with a dilucot, essentially starting from scratch (
this link is our friend). Or maybe just a little slurry and half of a dilucot. Or... Or...
Note that coti edges LOVE the strop. For the exact same hair, I've experienced an edge that goes from a violin HHT pre-strop to a easy-popping HHT post felt and leather. Don't get to discouraged until after you've stropped it.
It sounds like this is still your only straight at this point, so be aware that every time you try something new, you
might make things worse. Not that it can't be worked back (happens often enuff), just that if you get frustrated with it, you may not be able to straight-shave until you fix it, have someone else fix it, or buy another shave-ready straight. Making things worse is a Good Thing, as that forces you to learn your way out of it. Now, trust me, some razors can give you fits. If so, pay attention to your attitude and stop the honing session. Better to wait for another day than make things even worse ;) (yes, experience talking).
This is NOT to say don't do it. It is highly encouraged. You're at the point where everyone gets: far enough in to know kinda the basics, ready to learn more, and want to dive in. Great! But remember that you need a constant in your journey at this stage, thus having an extra shave ready razor you can fall back on is very important in the whole learning scheme. I'd say go for it with your new coti, and do whatever you want, but only if you have a backup edge you can trust to get you through it and be able to compare
your edge to.
Good luck!
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