You'll need different "scenes" from the ones you used to do your recording (though keep those for when you do recordings later).
Set up a new scene and call it "stream live" and add your webcam to it as a source. Make it all look like you want it to look in the preview, then "lock" the webcam in the sources list so you don't accidentally move it around anymore.
Get VLC 64 bit here:
https://www.videolan.org/vlc/download-windows.html
This is a media player for playing video and audio files. The nice thing about it is that it also has hooks for using in OBS.
Once you install VLC 64, close and re-open OBS (if you had it open), then make a new scene and call it "Play video".
Add "VLC Video Source" into the empty source list. Add the videos you want to play into its "playlist," and decide what you want the player to do when you don't have this scene loaded (Stop, then restart from the beginning, or pause and resume). Then set up the scene with how you want it to look (IE, make the video that should now be playing as taking up the whole window, probably).
So now, how basically this will work, is you start off on "Stream Live" and it works like you are used to... then when you're ready to play the video, you switch the scene to "Play video" and what's in the preview window there will go out over your stream instead of your webcam feed. It will play through all the videos in your playlist, so if you have more than 1, that will work. Then, when you are done with those videos, click "Stream Live" again to resume normal webcam broadcasting.
You can do a dry run with all this in OBS without actually streaming it. You won't be streaming unless you set up the RTMP and then click "Start Streaming." You could even prerecord a stream this way by hitting "Start Recording" instead of "Start Streaming" and then upload that to youtube or something.