With the tonometers we use for home eye pressure monitoring, there is nothing that stays in contact with your eye, unlike the Goldmann tonometer used by most ophthalmologists. The Goldmann stays in contact with your eye for an extended duration. Your eyelid could contact the prism of the Goldmann tonometer.
The Icare HOME tonometers (including Icare Pro, TA01i, etc.) do not stay in contact with your eye. They have a very gentle rebound mechanism. The small probe bounces off your cornea in an instant. You generally do not even feel it and it is quicker than a blink.
The Reichert tonometers (including 7CR) do not contact your eye at all. They use a modern and gentle air puff. If you blink, the tonometer will prompt you to repeat the measurement.
Generally, there is no need to hold your eyelid up and out of the way of the tonometer.
However, with home tonometers, it is possible that eye eye lashes could get in the way when you blink. It's not usually a problem. If you feel more comfortable lifting your eye lid up with a cotton swab, that's OK. You can do it as long as you know how to do it properly.
The cotton swab should not touch your eye, not even through your eyelid. It must only contact your the skin above your eyeball. Using the cotton swab (or anything) to lift your eyelid requires skill.
It is quite possible that your doctor will be willing to demonstrate the proper method to you in person and even allow you to hold your own eyelid up when he or she checks your IOP -- my optometrist happily helps me with things like this.
Alternatively, you could open more widely for the brief instant required to conduct a home IOP measurement (which is quicker and easier than a Goldmann measurement). Even the "open wide" method needs to be carefully considered. You could alter your IOP by straining to keep your eye open wide. Don't strain. Be relaxed.
Mostly, you should just relax and not worry about doing anything like the above. We generally do not need to do those things with home tonometers. Do remember to breathe normally and relax.
In my case, I do often notice that my eyelashes will contact the Icare probe when I blink before I measure. This does not affect the quality of the IOP result.