I want to use my laptop for running these old games but I'm not sure if they will work without a "proper" mouse? Does anyone have any experience of using a laptop?

AFAIK, most laptops have an option of attaching external mouse via COM, PS/2 or USB. Check if your has.

I use my notebook for all games that you can imagine. It´s no problem to use the touchpad for games. But it´s sure more comfortable to use a real mouse. I use a normal infrared mouse with the receiver connected to the usb ports. You don´t have to buy an extra notebook mouse. It´s even possible to use an external keyboard. For some games that need thr numpad it´s quite clever to make use of this opportunity...