I googled "simple 555 timer circuit" today whilst researching some stuff for my electronics CW, and found a diagram that has a solenoid and stuff on.
Might be worth having a hunt and seeing if you can find it.
Instead of having a programmable dwell, you could just have the timer circuit made so its on for however many ms, and off for a lot, giving a basic circuit that activates the solenoid for a set amount of time every time the switch is activated.
For CW, if you make a circuit and its well thought out and developed, and works on paper, but doesnt work on your project, you'll lose 4 marks out of 100.
4 marks isnt much to lose.