The Export tab and Exported dialog let us set Existing Files to "Skip", "Add Suffix", or "Overwrite" in the Export Location tool. There appears to be no way to set this via AppleScript on macOS.
Would perhaps look something like this:
tell application "Capture One"
tell tool "Export Location"
set existing files to {one of "Skip", "Add Suffix", "Overwrite"}
end tell
end tell