I found out that Fritzing is actually sufficient for my needs. It's not very convenient, but acceptable.
It's also not very obvious how to do it, so here's a short description of here's how it works:
- Delete the default bread board
- In the "core parts", find the "basic single-sided stripboard" or the "basic single-sided perfboard" and add it
- If you need interruptions in the stripboard, click on the PCB wire to remove the copper
- Add the parts (resistors etc.) as needed
For someone to actually solder the thing, you need 2 views, one with the parts and one for the stripboard.
- First view: select the menu View/Show all layers

- Second view: select the menu View/Hide all layers, then show the breadboard layer. In that view, you'll see where to interrupt the stips:

Disadvantages of using Fritzing:
As you can see in the above images, the LED and the transistor use (much) more space than needed on the breadboard. Not all parts are available in top view, but you may use the LEDs and transistors I have designed.
The breadboard in shown in top view, but you will need to work in bottom view. For printing, I suggest taking a screenshot or saving as image, then flipping the image.