Long live Streets & Trips.
I still use it but I chip away at BaseCamp.
You can do exactly what you describe using the BaseCamp computer map.
In fact, your described method of placing way points might be easier than using the search function (because you already know where you're going).
First point in BaseCamp: --> Don't use "Trip Planner"
Example image:
1) Establish waypoints
You see that I have found Five waypoints shown in the bottom left window column. AND I have highlighted them by selecting them with the mouse.
2) After the waypoints were highlighted, RIGHT CLICK them to bring up
window two that shows "Create Route using selected waypoints"
3) Click "Create Route using Selected Waypoints"
Result: You will now see in the bottom left window column a new Icon in addition to your Waypoints. That new icon is your route.(not shown in above image)
RIGHT CLICK that new icon and select OPEN
That will bring up your route planner like this: (sorry, this image was a Jeeping trail - but
it will show all your waypoints and you will find many options for manipulating them.

The above instructions, though sketchy, are enough for the determined and careful map user to figure out the basics of BaseCamp.