As the saying goes, "Control what you can control." You can control the pants situation (wear them) but easy access to a radar gun for the average baseball family to use for a day to shoot a video I don't think is a reasonable expectation.
I highly recommend "looking" like a ballplayer though when introducing yourself to a baseball coach via a recruiting video. But the radar gun in screen? It's nice, if you are throwing 85 or more, but 84 and lower is not going to help you, especially if you are a current Jr. or Sr. Won't hurt you in many situations but it isn't necessarily going to help you in all cases. So I'd leave it out.
Additionally, access to a radar gun is difficult for most baseball families. Expensive to own and difficult to borrow from someone or some organization. Trying to nail down the use of a gun could postpone a current Jr. from getting a video out for another month. Time a Jr. does not have right now.
My RHP has never had a gun in his videos and has gotten plenty of interest as a freshman and sophomore. Granted as a younger player they want to see mechanics, size, and projectability.
I believe this young man is a Jr and because of that I will concede that velo is something a coach will want to know sooner than later, I'm just not sure you need to provide it up front in an introduction. May help the coach in his initial screening process of what emails to keep and which ones to delete, but won't help your cause as a prospect if the velo numbers are say 84 and south. Obviously this all depends on whether you are an LHP or RHP, size, age, and most importantly what caliber of baseball school you are targeting. Plenty of RHPs and LHPs in "college baseball" sitting 80-84 as there is a wide variety of levels of college baseball. I will venture to say, most coaches will assume you are south of 85 if they do not see a radar reading in frame. Nothing wrong with that.
Conversely, if you are 85 and north simply providing a PG profile page with velo numbers or online posted showcase velos is another way for an 85 and above prospect to provide velo #s to coach. I wouldn't waste time trying to borrow a radar gun, or money by going out and buying one. Not cheap. Bottom line, if you got it, flaunt it. If not, I'd leave it out.
I say, don't worry about the radar gun. But wearing baseball pants is a must for this arm chair director. Otherwise, I thought a very good video.