Make all those videos private or add them to a new playlist and make them private there.
Next visit this YouTube Help - Allow others to view private videos:
About Privacy Settings (Video Instructions):
Private videos and playlists can only be seen by you and the users you choose. Your private videos won’t appear to others who visit the "Videos" tab of your channel page. They also won't show up in YouTube's search results.
To share a private video:
- Go to your Video Manager in Creator Studio Classic.
- Find the video you want to share, then select Edit.
- Beneath the "Privacy Settings" drop-down menu, select Share.
- Enter the email addresses of people you'd like to share your video with, then select OK.
Comments are not available on private videos. If you want to allow comments on a video that's not publicly available, change the privacy setting to unlisted.
The first link includes instructions for: desktop computer, Android, iPhone & iPad.
The difference between private and unlisted is that you can share an unlisted video's URL with other users. The people you share the video with don't need a Google Account to see the video. Anyone with the link can also re-share it.
Contrary to what is mentioned in some of the comments below you can have private videos and choose who to share them with.
You can also create a Brand Account and either use your existing channel or create a new linked channel, transfering the videos to the new channel.
You can add Managers to the new channel, allowing them to access the private videos and have basic management capabilities, if you want them to be able to more than simply view private videos.
The above is applicable to one or more additional people, beyond the creator of the channel.