Don't think you can position the cursor inside a web viewer.
What exactly are you trying to do?
(There may be another way to do what you want as you can build reports in a web viewer via a script that uses Set Viewer to send text with HTML tags to the viewer.)
Pretty simple really. The operator needs to paste some values from the db into some fields on a web page. Seemed like the simplest thing was to use the webviewer, the operator puts the cursor in the name field on the web page, then if I can get the contents of some field onto the clipboard and trigger a general paste (as opposed to the field specific paste in script steps) that would to it. Then they put the cursor in the address field on the web page, click another button, etc. I can do Ctrl-V into fields on a web page in a web viewer so I know pasting into it works.
As I went through all the script steps and functions I really expected to see a "copy field contents to clipboard" and a generic paste, or maybe even "paste the contents of field x", but don't find anything like that. Local and global variable don't seem to be able to be pasted or moved to the clipboard either. Is this just not doable in FM?
Not do-able as you describe, no. But depending on how the web page is set up, you may be able to specify the contents of fields from your database to supply data to the web page automatically. This is how you can set up Google maps, for example to display the location of an address stored in fields in yoru database.
(Scripted copy and paste aren't the best options in terms of general interface design as they destroy any data the user may have copied to the clip board and this something that your users can find to be very annoying.)