While I can't really speak to your question about removal, it seems like you could be safe by checking where your strings are when you insert the cup. Like making sure the strings are inside the cup? Also, my guess would be that since it pops out so easily upon bearing down there isn't much, if any suction, which is good.

I have my strings cut to 1/2 inch, and they have migrated upwards so that most of the time it seems like they are at most 1/4 of an inch sticking out of my cervix, and a lot of times I can only feel them by pressing into my cervix opening. They only go lower during my period. My partner has felt them once or twice, but never experienced pain. It seems to me like the strings are sort of blunted. The only way I can describe this is like you know when you burn nylon string or something the end of it curls a bit? That's what mine feel like, just the very tip, 1 mm or 2 is blunted and curled and this seems to make it less pokey. I don't know if that's something my Nurse Practitioner did on purpose since I told her I was using the cup, or if it's the way all strings feel.

HTH!

I've used Insteads and now a Diva without any issues at all, my feeling is it's not so much the suction as getting the strings caught and I generally have the cup right over the top of my cervix.

I gave you my useful info over at iud_divas.
Just wanted to add that as long as you don't actually pull your strings, it's pretty unlikely that your cup will cause you to expel your IUD.

I have a small Lunette cup that I trimmed all the way down, stopping at the last "line" on the stem. I cut cleanly and use an emery board to smooth down the edges. I've not had any poking issues since.

As far as removal goes, I just tuck my strings as far back in to the crevices of my vagina while I am on my period. Check them every day or so and push them back in to the corners! Like you, I bear down to remove the cup, and it seems to me that if the strings did catch on the cup, you would feel pain as the tugged out. Puling the cup out manually is much more likely to result in a string catching and you will likely be pulling too quickly to stop if there's a hint of pain.