Some Cessna flap switches of that series and era were required by service bulletin to be changed from the "hold it to go down, but it will hold itself to go back up" type to the "hold it both ways" type. This was a corrective action for flap motor limit switch failures, where the pilot would have no idea that the flap motor limit switch had failed, and the motor continued to run (or attempt to) after the flaps were fully retracted. This often resulted in something expensive being burned out, and the flaps not being available for landing.
Thus, the flaps of the affected Cessnas will only move if you're holding the switch. This made the preselect systems popular by comparison, though they had some limit switch issues of their own.
The speed with which the flaps move (or time required to get them from one extreme to the other) is governed by several several factors. The motor "coasting" to a stop after power removed is one. The faster that the flaps were moving, the further they'd coast (uncommanded position, and hard on the mechanizm, when they reach a limit). More importantly, there is a controllability requirement with sudden and total flap motion. For those Cessnas with manual flaps, it is possible to move the flaps from 40 to zero instantly, and at a slow speed in flight, this can create a sudden (and non compliant) drop if the pilot is unwary. The slower cycle time for the electric flaps assures that controllability is maintianed with any pilot controlled use of the flaps.
I suggest that you are looking for 10 degrees, rather than zero, for most takeoffs, in accordance with what the flight manual says. Though not approved in the flight manual, if you become airborne again with flap settings a little greater than 10, the world will not end. I do commend your using 40 flap for landing when ever you can, that will give you better landings, and save people money and risk. My experience, as recently as yesterday, is that with appropriate skill, lesser flap settings are not requried for safe crosswind landings. I agree that the flight manual says otherwise, though flap settings are not limited for crosswinds.
If the "pilot workload" is too great for reconfiguring the aircraft during a touch and go (particularly with runway length a factor), perhaps touch and goes in those circumstances are unwise, paticularly solo. Though capable, the aircraft was not designed to be pilot friendly for touch and goes. It was desinged to be landed and stopped, then flap position changed. There is a requirement for full flaps go around, but in that situation, full power would have been applied first, then with the throttle locked at fully open, you have a free hand for the flaps (don't raise them all at once). Re trim as required.
Go around is another reason that the "held in the up position" switch was not liked, as, with a very slow go around, the pilot could switch to "flaps up" and forget to interrupt the retraction. In one motion, from 40 to zero, the aircraft could easily settle, and the unwary pilot, already overloaded, would not be able to climb away. This is why the manual flap Cessnas (all 180, 185's, and all very old 100 series) are still safe, as if the flaps are in motion, your hand is on the flap lever, and you can reselect instantly if you need to prevent settling.
The manual flaps are very well liked in the 180/185 floatplanes, where "modulation" of the flaps on takeoff is employed by some pilots. Also great for instantly killing lift after touchdown.
The switch is a "Momentary Contact, double pole, double throw" type.