At that point there is no correcting the timer, you need to either play the run back and retime the run that way, or you need to frame count the run to get an accurate time. In other words, the only way to get an accurate time is through some kind of retiming in post production of the run.
As an aside, I would highly recommend putting the pause key for your timer far away from any other key so that way something like this doesn’t happen.
Keep in mind that most leaderboards don't require you to have a timer in the video, since human-controlled timers will always be inaccurate and are mostly for convenience's sake. An accidentally paused timer shouldn't stop you from submitting a run (in ideal circumstances).
Yeah that’s a good point - the timer is irrelevant, as long as you get accurate time, that’s what matters for the submission of a run (unless otherwise stated by a game’s rules).