You can set up LiveSplit to automatically start the run and split for each finish, while the timer runs in real time as normal.

Download LiveSplit from the official website: https://livesplit.org/downloads/ Do not save or extract LiveSplit to a folder that require admin permission, like Program Files. Admin permission seems to stop LiveSplit from talking to it's servers, resulting in the auto splitter not activating. I recommend using the My Documents folder instead.

Right click the LiveSplit window and select Edit Splits. Type in Kackiest Kacky 1 as the game name, and then click on Activate

Make sure to set the comparison for the timer and splitter to "Real Time". This can either be done when editing the layout, or by right clicking the LiveSplit window -> Compare Against -> Real Time.

Simple split-files and a layout to use with the splitter can be downloaded here: https://www.speedrun.com/kk1/resources/j1t6p