How can I print just the waypoints on a route?

I haven't been able to find a way to do this in BaseCamp, however it is relatively easy to do if you save your finished route as a GPX file, then import it into Garmin's older MapSource software.

Select your route and open the route property dialog box. Select all the rows in your route, then copy and paste them into Excel. The paste of your route will be into individual cells rather than all the fields into one cell per row as with BC. This will give you the data with all the distances, timings etc in a form that you can easily delete the shaping points.

Add column filters, sort on the Directions/Name, then delete all the rows with turn-by-turn instructions "Turn ...", "Get on ...", Continue ..." etc to leave just your waypoint rows and then re-sort them by row number and print it out to put in your tank bag.

If you right click on the route, choose OPEN, Click PRINT at bottom right, then click PAGE SETUP at top menu, then Under MAP DETAILS Leave MAPS checked, but down below that Uncheck all the items under ROUTE DETAILs. Print Preview shows it doing what you want.
Actually someone on this forum showed me this last week when I wanted to only print the directions and not the maps.

Doing that, all I see is the map.

Yes I already tried that approach but I could not see a way to select only the waypoints and timings for printing as per the OP's question, BC will only print the full route directions.

RE: Gary:  
Oh sorry, misunderstood your question my bad. Appears yours and Eyelet99's are only methods for that. I could not find it either after fully comprehending what you wanted.

Basecamp does not provide that feature.

If you use Windows 10 the simple method is to make a screen shot of Basecamp's route calculator.
In Win 10: press three keys in sequence:  Windows key, Shift key, "S" key.
That will bring up a crosshair which you use to select that portion of the screen that you want to copy.
Copy it and save it to desktop as a jpg file.  Then print it out.
 

Juat asked Garmin the samething, so while waiting for them to respond I remebered I had purchased an app "Able2Extract Professional" a few years ago to convert a PDF file in to Excel, it also converts it Word and many other formats. I unticked maps and statistics and the printed the out put to "Microsoft Prnit to PDF" which saves it as PDF file to you local drive. I then, within Able2Extract, opened the PDF file and converted it to Excel then once in Excel I then deleted all the turns etc and just kept the Via Points along with the milages for each of these Via Points. It's a bit of a faff but I hope this helps.

After a few tests I have found that the best option is to Screen Snip the Via Points etc within the properties tab then paste the snip into a word document, save it as a PDF file then using Able2Extract to extract the data from the PDF file and extract to Excel. Its OCR is not 100% accurate but at least all the data is present, just need a little time to sort out any misaligned data. If Via Points extend past the bottom of the properties window, then do a 2nd snip and treat as a separate PDF file and combine in a separate Excel file.