Wico made no switchable sticks in the sense that T-Stick+s or OmniStick Prodigies are switchable. Wico 8-way sticks also came with a 4-way actuator, so that the stick wouldn't register diagonals. But you don't get the feel of the 4-way restriction when used this way, and it requires opening your control panel and partially dis-assembling the stick to make the swap, so I don't think that's what you had in mind.
Wico handles will fit Happ Perfect 360 joysticks. P-360s also come with both 4 and 8 way actuators, and also require opening the panel and partial dis-assembly to change. Other than that, Wico handles will fit the Chineese knockoff el-fake-o "Wico Style" joystick base, but you wouldn't want to use one of those. As for official Wico, there are leaf and micro versions of the Wico base out there. The leafswitch type comes in a dedicated 4-way version as well as the standard 8-way. I don't know if the microsiwtch type was ever offered in a 4-way or not. One might be able to mate a 4-way top half from a leafswitch base assembly with a microswitch bottom half to make a 4-way microswitch stick.