There are lots of bits and pieces to unpick in the question "have other countries who have introduced self-ID had any problems?"
Firstly, how would we know about problems? Who is going to tell us? I suspect in many cases women who would have accessed services that are now provided by / dominated by / accessed by transwomen are simply not accessing those services or going underground. I don't know if there's an informal women's refuge network in somewherelike Canada, but it wouldn't surprise me that something like what we had in the UK before proper refuges were set up (where a friend knew a woman who knew a woman who would provide a bedroom for a few nights so that you could leave your abusive DH) had sprung up. By its very nature, this wouldn't be reported in the mainstream press.
Similarly, are women changing their behaviours by not using public toilets / changing rooms / similar, because now that they are not single sex spaces they no longer feel safe to do so? Who is monitoring and reporting on toilet usage? (I'd bet no-one)
Secondly, there is always a time lag with things like official statistics. If as a result of self-ID there is a spike in "women convicted of rape" type incidents, there will be a delay in fully understanding what is happening as official data takes a while to be collated, cleansed, analysed and then published.
Thirdly, there is a natural lag with seeing the full implications of such a far-reaching shift. How many female NHL players are actually trans? The number at the moment (I believe) is 1, and it will be a number of years before the impact on women's sport really filters through so that sports like ice hockey are dominated by transwomen. Meanwhile, the damage to female athletes will have been done and will be irreversible. Women will miss their physical peak, their opportunity to shine in their sports. They will miss out on the college scholarships (and thus, in many cases, a college education). They will never get that time back. By the point at which the authorities see that the women's team is mostly comprised of men, they will be back to days where there were no women's teams and have to start all over again - if they even bother.
Fourthly, different countries have implemented self-ID in different ways. Notably, the legislation in Ireland excludes prisons from the scope of self-ID, so of course they won't experience the sort of issues that we fear would arise in the UK. (It also excludes transmen from becoming Catholic priests, which is not as pertinent in the UK as it is in Ireland, but rather illustrates that the legislators don't really believe that it's possible to change sex)
Finally, I believe that it shouldn't matter if "only" a few women are harmed by those who will abuse self-ID. It's entirely predictable, and I find it hard to think of another policy area where it would be OK to say that there is an "acceptable" number of victims. One victim of the policy change is one too many. Anyone who thinks otherwise is by default saying that there is a threshold that it is OK to stay below, and they should be challenged to articulate this. Is it OK if 100 women and girls are abused as a result of self-ID? 1000? 1,000,000? Where should we draw the line?