I agree, but I think if you do that, you should accept the employer having the right to potentially be able to see that information.

In practice, from doing many of these investigations, no one bats an eye or gives a single shit about what kind of non-work activities you're doing. The visit to the ticket website would just be a few entries in a long list of other web visit entries, which we'd quickly scroll past while trying to find the thing we're actually looking for (usually malware-related traffic).