That's basically what the DNC is doing in Hawaii. The congresswoman who died will remain on the ballot and if she wins, an appointment will be made by the DNC.
There is no provision for "appointing" a Representative. The vacancy must be filled by special election. Votes for a deceased Representative should be thrown out.
Nobody, but nobody, can make an "appointment" to the House of Representatives. If Mink stays on the ballot and wins, the Governor of Hawaii will have to call a special election.
Check out Article 1, Section 2
When vacancies happen in the Representation from any State, the Executive Authority thereof shall issue Writs of Election to fill such Vacancies.