So I started running this game on the Switch, but I don't have a capture card yet. When I pick one up in the next few weeks, should I keep my current splits displaying my pb, or should I reset my pb to whatever I get on my first recorded run?

Splits are not important. You can save all your attempts in LiveSplit, the time is counted directly at the submitted run (even without splits). Splits it's an auxiliary thing for you and the moderators, nothing more. So feel free to use this program as you want. Good luck on your attempts :)

Thank you for the quick response and for the good luck. I'll just let my splits be and continue to work on my time until I get my capture card. Thank you. :)