Turning off Snap Tips, while leaving Snapping On, does not seem to be possible in ArcGIS Pro 2.1.2 (which I am currently using) or earlier versions because these are the only Snapping Options available:
In comparison, ArcMap 10.5 has these Snapping Options that would help you, if you were using the older architecture:
Unless turning off Snapping in ArcGIS Pro is an option for you, it looks like seeing Snap Tips is unavoidable.
To have this changed I would recommend that you submit an ArcGIS Idea.
I have upvoted your ArcGIS Idea but so far only three people have expressed an interest in it.