As Atif butt82 requested a schema to be drawn via a PM here it is.
Most portable fans have 4 switches, mechanically interlocked ( drawn in the box of schema ) to get 3 speeds. Leave as it is.
Celing fans may have a capacitor arrangement with a rotary switch or an autotransformer.
Add the extra switch and capacitor C 3.
By choosing the correct value the desired low speed can be obtained.
A bit of experimenting may be required.
The X2 class mains rated Caps work great. My room ceiling fan has 2 x 0.47 µF 250 Vrms in parrallel for C3 to obtain the lower 3 speeds.
(That is for 240 V 50Hz.)
As said before, you are working with lethal voltages so ensure that all wires are mains rated and sleeved so no danger of electrocution exists.
Hope this helps,
Regards, Raymond