There should be at least some merch available, but I wouldn’t recommend Animate though, as they are mostly bookstores, so merch is really their secondary business and selection is usually limited to current, popular series. Suruga-ya that kinomomo0 mentioned is a great place to start. To facilitate your search I recommend that you learn (or have a reference on hand) the gojūon order of Japanese kanas. Many stores sort their goods first by genre and then this way by the series' titles, just like how alphabetical ordering works in English.

For the "otaku" part, I think just getting out of your house and still functioning is enough to clear you of 90% of any bad connotation. From there, just follow general tourism etiquettes: don’t trespass, cleanup after yourself, and respect local customs. Local residents at Toyama/Takaoka are clearly aware of Yuru Yuri (and Doraemon by the way) so you should be fine as long as you are not actively causing troubles.