How can I find the cheapest flights to a small airport that isn't in the ITA matrix (e.g., for a flight from Seattle airport to Point Hope airport)?

In order to get to a place like Point Hope, you will not be able to buy a through ticket, and must instead buy

• a ticket to the airport with scheduled airline service, which in that case is Kotzebue Airport (OTZ), and which you can buy through normal air ticket channels, and
• a ticket from that airport to your final destination. In your case, Wikipedia says that the only carrier on the route is Bering Air, which as of this writing operates two flights daily to Point Hope. The latter of the two flights leaves at 2:45pm, so you must arrive at Kotzebue before then in order to make the connection.

Small airlines like Bering Air are often expensive but usually do not mess about with flight prices as much as large airlines, so the big cost differential will come from the "normal" part of the trip, plus possible costs for overnight accommodations if your flights do not work out for a same-day transfer. For example, Bering Air currently is asking $295 one way or $531 round-trip for a flight on the OTZ-PHO route, with no cheaper or more expensive fares available any time within the next several months (though flights can sell out).