In reply to Flinticus:
Depends on your definition of "OK" or what you're worried about. Probably the most likely bad outcome is that the YouTube video gets deleted at some point and you end up with a dead link. But that's not going to do any real harm other than make your website look mildly less professional.
You could argue that directing people away from your website rather than keeping all the information self-contained makes them more likely to get distracted and not come back (presumably you ultimately want them to book some kind of service with you?). YouTube is certainly full of distractions, maybe they end up watching a load of cat videos or maybe they watch another video about the topic of your website and like the look of that person's service better than yours.
But if you're worried about the YouTube link being redirected to something nefarious, that couldn't happen. In principle, the person who owns the video could replace it with a different video, maybe one less savoury, or add inappropriate links or text to the video description. But that would violate YouTube policies, putting their account and reach at risk. So it's maybe worth considering as a remote risk if the video you want to link to was posted by some kind of dubious content mill, but if it's an original creation by someone with a substantial profile on the site, it'll be very safe.