A very uncertain guess places the capacitor at 4.78 uf.
A 5 uf capacitor or less is where I would start.

 

I will keep it in mind for the eventuality that I don't find a ready made suitable inexpensive dimmer.
What would be the uf range that I should check? What would be the upper and lower uf limit according to your best guess?

Another question. In case I would use a light dimmer and put it into a circuit with a capacitor. What is your assumption about the light dimmer circuit? Are you assuming that the light dimmer is a TRIAC dimmer?