is this doable if you don't have a speedrun timer or no

As long as you have video evidence then we can use that to calculate the final time. It's easier for us to verify if you can use Livesplit though, either during the run or adding it to the video later on.

Runs are timed in RTA, so yes. You don't ever need a speedrun timer for RTA because, well, the VOD length is literally good enough.