An option with Windows 10 that works for me, with the newer Paint 3D (in previous Windows versions, it was just Paint)...
- use either a screenshot of the map (IIRC it's now called the snipping tool in Win 10, instruction is provided with searching), or a photo of the paper map.
- view the jpg or whatever image on the screen, then right-click on it and open in Paint 3D, or the older Paint.
- in Paint 3D, select the tools for artwork, for drawing lines... it might take several tries to find the right tool.
- the brush tool seems to produce smooth lines, select appropriate color.
- draw the line on the map taking care to create a smooth line.
- use "save as" to save the new image to whatever folder the photos are being kept in.
- in the older Paint, the lines will be more jagged and more care is needed. Maybe there is a smoothing tool available, but I haven't found it in older Windows versions.
I'm probably leaving something out but that's it more or less... gotta do some work for now. I've been able to draw some nice, smooth lines with Paint 3D... back later if there are any problems.