Maybe: you don't actually have to remove it from the first hub first. You can just reset the device, then pair it to the second hub. That way, it will still be around (but not functional), and you can swap out the original device with the Hub Mesh device at your convenience without breaking any apps that might freak out about deleted devices in the meantime.
The Settings > Swap Apps Device feature could also help with something like this. I seem to remember this not working with Hub Mesh devices in the past, but they are showing up for me now, so I may have been thinking about something else (you don't need it to swap two Hub Mesh devices with each other--that can be done in Hub Mesh itself...not sure if it was that?). If that works for you, it would save the need to manually swap the old Zigbee device with the new Hub Mesh device. Otherwise, the "old fashioned" manual method is certainly always an option.
I'd say whatever is easiest for you or suits your preferences best, unless you see some reason to do otherwise. Maybe you only want to set up webCoRE on one hub, or maybe you want to keep apps and devices on the same hub as much as possible. Either way can theoretically work.
Regarding the App Stats you reference, I don't know what particular statistic you provided, so it's hard to comment, but in general, you're probably OK if you don't notice performance issues on the hub (what these exist to troubleshoot in the first place) or, if you want to be proactive, nothing stands out extraordinarily (high percent of total is probably one of the most general stats, but again, there are no hard and fast rules for what's "high"--though FWIW, everything I checked just now for me was mostly well under 1%).
Rule Machine is generally probably more efficient, but how much that difference affects real use may not actually matter. (Again, if you do notice problems, App Stats is one place you can start checking.) The most efficient option is generally a purpose-built app, so I'd consider things like Notifications or even Basic Rule first if they meet your needs before either of these -- but lots of people use webCoRE with success on Hubitat, so you won't be alone. Its current de facto maintainer for Hubitat has done a good job at making it more efficient, and the warnings you see from a few years ago suggesting to avoid its use entirely or risk slowdowns, lack of support, etc. are generally no longer applicable (though Hubitat does not officially support custom apps, so it's still technically on you, whereas they can fix problems with Rule Machine ... though there's no fixing the fact that either allows you to create arbitrarily complex automations with the ability to impair your hub if you design things poorly 
).
