“Last Tishrei, I began saying one perek of tehillim a day.”
Hah! I knew you’re not that biggest baddest worstest horriblest terriblest rasha ever!
“After all, if we’re not supposed to say it in davening, then perhaps it’s better to skip it altogether and not say it on that day.”
Some people say the entire Tehilim every day. Including on Yom Tov. So, clearly, it is appropriate to say.