I haven't used OneDrive. But if copying a file to a certain folder counts as "sending" then you could easily set up a batch file along the idea OneNoteSend.cmd:
Once you have the batch file working as desired put a shortcut to it in SendTo instead of the OneNote shortcut.
rem set filename to entire command tail
For %%A in ("%filename%") do (
rem echo.Folder is: %Folder%
rem echo.Name is: %Name%
ewm change "x:\OneDrive" below to the OneDrive Folder Path
copy %%A x:\OneDrive\%Name%
rem delay 2 seconds
ping 192.0.2.2 -n 1 -w 2000 > nul
rem Open File
Edit: To test the batch file open a command prompt and run it with the path of the file as in
for best results put the batch file in a folder in your Path.
I have a folder C:\Utils
that I added to the start up Path environment variable for my user account.
Stand alone exe and batch I dump in there.