What shutter can fit a lens element with large glass?

Your shutter only needs to be big enough to cover the sensor, not the front element of the lens. There are many lenses out there that have much larger front elements, but the image circle by the time it passes through the lens mount is a fraction of the size of the mount, typically a bit larger than the sensor, to reduce vignetting. That said, medium and large format cameras obviously have to have larger shutters to deal with their larger sensors...

A hat is the stylish photographer’s traditional front of lens shutter (and lens shade) though a press fit lens cap with a handhold in the center provides better control. Of course low sensitivity film/sensor and narrow apertures are needed when photographing in bright light due to the slow shutter speed.

Packard shutters are a pneumatic alternative that can provide a faster speed of about 1/8 second and can be front mounted.

Do it yourself options might include a rotating shutter similar to the design of movie cameras or a gravity powered knife shutter with an adjustable slit. It is more a question of desire, will to conduct wonky experiments, and engineering skills than anything else.

Even a leaf shutter can be pretty simple. Take a look at a Holga or Diana. The shutter is a couple of plastic blades and an unimpressive spring.

From a design standpoint, the smaller the maximum aperture the smaller the shutter can be. The same is true for shorter focal lengths.

I am assuming that if I use a shutter of a smaller diameter than the lens, the properties of the lens will change (for example, it will become less fast), because of the smaller aperture ring behind it?

That is not necessarily the case. The physical size of the aperture is (almost?) never the same size as the objective lens element; because its physical size is not what matters. What matters is whether the aperture obstructs the path that the light must follow while being focused at the image plane. That is the aperture's apparent/effective size as seen/magnified by the objective element (which is called the entrance pupil).

I.e. the aperture is (almost?) always a physical restriction; but what actually matters is if it is an optical restriction or not.

If the aperture diameter appears to be the same size as the objective element (due to the magnification of it), there will be no optical restriction to the light travel, and the lens's f-ratio/maximum aperture will be determined by the diameter of the objective element itself (it cannot be any larger). And if the aperture appears smaller than the objective element, then the lens's f-ratio will be determined by its apparent diameter because it is smaller and it is an optical restriction.