Probably not. And you probably won’t really want to do so when you consider what would be involved.

Theoretically you don’t have to register if you don’t directly or indirectly solicit contributions from residents within the jurisdiction. But the regulators won’t believe that you don’t solicit. You don’t have to solicit directly in every contact to create a solicitation when considering your entire range of contacts with a donor. That, at least, is the view of most regulators.  You clearly have solicited in the state in the past. You will be having other contact with these donors in the future.  It would be virtually impossible not to indicate that you would be happy to receive additional contributions from them. And you could certainly use the money.

If you are soliciting in any other state, you would want to send a different annual letter to the states in which you are soliciting than you would send to the state in which you are no longer soliciting.  The cost of that differentiation alone might be more than the annual registration fee.

And what about your website? Some states take the position that having a “donate now” button on a website is in itself a solicitation, even if you never receive a penny from their residents. Are you prepared to remove the donation mechanism, or disable it for residents of this state, or return the gifts from anyone in the state who gives?

If you want to stop soliciting in the state, you would still have to file a final report. Your failure to renew might cause the regulator to ask some questions. If you can convince the regulator that you are no longer soliciting in that state, which might be very hard to do, you then have to live up to your commitment. You could not solicit any resident of the state in any form at any time during the year. That means everything you send into the state has to be totally divorced from solicitation.  And that means fewer contributions. And that means less revenue with which to pursue your mission.

Everybody knows it is a pain to file these forms, but it is part of the price of doing business in the charitable world.

It seems to me you have two options. You can continue your current operations, file the form and pay the small fee.  Or you can spend the time and money to change your entire operation, cripple your fundraising from your strongest supporters, and when you lapse (when, not if you lapse, because it would be almost impossible not to solicit somebody within the state) face an investigation, possibly an injunction, and probably a fine of many multiples of the annual filing fee.  Plus an order to re-register, file the annual return and pay the annual fee. Your choice.