Some newer calibration-friendly wide-gamut monitors have sRGB emulation modes (I know my Eizo does, I know BenQ does, and makes it extra-easy with their "hotkey puck", and I suspect some of the NECs and Dells do as well). I'd create a version of the image just for export in Lightroom (or C1, etc.) - probably resize at this point so I could see the sharpening as well, flip the monitor into sRGB emulation mode, and edit to taste.
There are two MORE unfortunate considerations - one is that many Web platforms perform an additional server-side compression step you have no control over. They certainly often resize, and some may also mess with color.
The second is that many devices have sub-sRGB gamuts and no color management at all. Almost all Apple devices going back a long time are at least sRGB and have a factory profile, and both Macs and iOS apply some color management at the OS level. Many inexpensive Windows systems and Android phones/tablets have gamuts as small as 65-70% of sRGB, and Windows has no OS-level color management (I don't know about Android). All serious imaging applications on Windows ARE color managed at the application level, but most browsers are NOT.
If you know your target is newer Apple devices (last couple of years) - say you're e-mailing images to a client whom you know uses a 2015 (or newer) iMac, you can still target sRGB, but you can also target a somewhat wider color space called DCI-P3, which is intermediate between sRGB and Adobe RGB. As far as I know, the DCI-P3 support list looks something like:
MacOS:
iMac - mid 2015 and later
MacBook Pro - 2016 and later (all USB-C/Thunderbolt 3 models)
iMac Pro - presumably at least DCI-P3(will it be Adobe RGB?)
NO MacBook or MacBook Air
Mac Mini and Mac Pro of course depend on the attached display (most Mac Pros probably have a wide-gamut display, Mac Minis could have anything, including a sub-sRGB display).
iOS
iPhone - 7 and later
iPad - all iPad Pro models except the original 12.9"
There are a small number of Android phones (and at least one Windows computer, the Microsoft Surface Studio) that also support DCI-P3, plus a small number of Windows laptops whose internal screen is at or near Adobe RGB (and a few Windows desktops with wide-gamut monitors. These are much less common outside the photographic and video world than the DCI-P3 Apple devices.
Dan