IMHO, unless the plastic UNDER the rivet head is deteriorating, leave it be. (But of course you can't really see it under the head very well). And unless you detect a leak.
The part of the snap cap base under the rivet head will help seal the hole. I would add a dab of sealant in the center of the rivet head (as it appears is done in at least one of your photos). That will stop leaks
through the center of the rivet (at least for a few years). I think the cap serves two purposes, leak prevention through the rivet's center and it just looks better. Poor appearance I can live with but you can stick the cap onto of the sealant if you want. Perhaps a good adhesive type sealant will keep the cap on for a while.
Again, this is just IMHO.. No doubt others will have differing or maybe even not so humble opinions.
I just replaced one of my rivets yesterday and I can tell you, things can go wrong. So why fix what in effect is not broken?
In my case I had a rivet installed on a new Scamp
where it did not grip the acorn nut very well where it attached the bathroom wall to the shell, so the acorn nut fell off in a few months after a few thousand miles. It also appears the hole in the fiberglass wall of the bathroom wall might have been widened by wear from the rivet. Note that the holes did not line up so the rivet was angled up a little from outside to inside.
This was not an immediate problem except it was holding the bathroom wall to the shell, so the wall separated a little and the sealant in the shower opened up. I don't use the shower but if I did, water could go through the separated sealant at the corner of the interior wall.
The rivet could actually be pushed out with little effort so I did that, and got what I think is the longest rivet that Scamp
uses (#16). Well, this one was a little short and did not grip the acorn nut at all. And due to my inexperience I kept pulling the rivet until it made a secure connection, but ONLY to the shell. The bathroom wall did not get fastened to the shell. (Note to virgin riveters below).
So I drilled off the head and tried to remove the rivet that now was not doing anything other than sealing the hole in the shell. This is when things got worse. The rivet was expanded between the shell and bathroom wall and I could not get it out of the way to put in a new rivet. I eventually had to stick some wire cutters in between the bathroom wall and the shell (covered with rat fur too making it even harder). Between cutting the rivet here and prying and pushing I finally go it out.
I installed the next # 16 rivet with a washer on the inside instead of an acorn nut because the rivet was still not as long as it should be and the hole might have been too large. Actually I tried to use the washer and the nut but only the washer got grabbed by the rivet. I also had to use a brace to push the bathroom wall against the shell, doing it carefully as to not do any damage.
It turned into a four hour project but I finally have the rivet installed with a washer. But even now it appears that the grip on the washer might be tenuous so I will have to see if it becomes unfastened. In that case I need a longer rivet, or might even go with a bolt and nylock nut for this troublesome location.
But that was just one rivet... if you choose to replace yours, maybe it will go smoothly.
Note for newbies at riveting: You need to have someone inside the trailer holding the acorn nut tight against the rivet and you start to pull it. I think I would suggest that the person with the rivet gun outside yell out the count for pulls.. ONE! TWO!.. etc.. and the person inside should watch to see if the acorn nut get grabbed. If it does not in one or two pulls of the lever, yell STOP and then reevaluate to see if your rivet is the right size. Hopefully you can stop a failed install before it becomes a hassle to remove the rivet.