The Appendices to The Lord of the Rings are apparently ambiguous on the date of Arvedui's death. Appendix A gives it as III 1974, the same year Arvedui's kingdom fell, but the Tale of Years in Appendix B gives the following year, III 1975.
Fortunately, the fuller story of Arvedui's defeat in Appendix A has enough detail to solve the mystery. The invasion of Arthedain took place in III 1974 'before winter was ended' (which can only mean very early in the year). The ship sent to rescue Arvedui only arrived 'after many days', and when it reached him 'it was then March'. So, this places all the action - including Arvedui's death aboard the stricken ship - during the first few months of the year III 1974.
In the original form of the story, found in volume 12 of The History of Middle-earth, the rescuing ship did not reach Arvedui for an entire year. That's the reason the uncorrected Tale of Years gives III 1975 for the date of Arvedui's death.