No I do not think it was important for Joshua to mention the sabbath, for the focus was not on teaching us about sabbath keeping but about, 1.) time frame for entering the promise land (tying it with the spring feasts), and 2.) in Jericho (the walls coming down.) Israel during the six day war in our generation, fought for their rights, and still keep mindful of the sabbath.
It is like the new testament, where since sabbath was as it was before the death and ressurrection of Christ, so there was no mention of the change of days to worhsip. it was not a issue that it is today. Even the gentiles accept that.... and waited until the next sabbath. No mention of sunday gather here.
If there was a change, and where there were changes, you will find them in the writtings of Paul, and in Hebrews where there was a change in the priesthood, the temple and it service, the understanding of the spirit of the law, and least important are the traditions of men, to name a few. But there are no scriptures that get into any change of the day of worship.
Sunday keeping would create an uproar in the Jewish community from which this message would have been first proclaimed. If you thought Yeshua was rejected before, if sunday worship is truth, He would have been thrown out even faster. The uproar over sunday keeping and sabbath of old would have been in all over the new testament, It is too significant not to be mentioned.
But it is not mentioned, there was no controversy over this issue. Every statement you find that it is used for sunday and sabbath arguments in the new testament are truly just references to time, season, and place. Since it never left the jewish setting established since Mount Sinai, it was not the focal point of any discussion of any of the apostles letters, or any writtings that any historial document outside of scripture. If God planned this, he would have prophecied it to be coming when Yeshua came. If Yeshua wanted it, He would have intstructed the disciples on it. Worship is too significant to not be addressed by the Holy One of Israel when He walked the earth as God in the Flesh. Every God had its day and the Holy One of Israel was known to have the Sabbath, in fact, He said, He was Lord of the Sabbath, identifying Himself with that time blessed and santified from creation and redemption from Egypt. Why did He not say something them, when He had the chance, about the changes He was going to make regarding the sabbath. The religious leaders were making sabbath keeping styles an issue. He could of pointed out prophecies in scriptures of the change, He could have shown them their errors regarding the day, but all he did is show them their tradition theology in keeping it was not in a loving and caring manner God would be happy with. Sounds like fine tuning what they already have, not a overthrow of what was established on Mount Sinai.
No evidence can bring forth until the 3rd century when political correctness of roman theology dictated it to be so. A little evidence of sunday keeping can be shown in the second century, but nothing before 100 AD. The writtings have been researched for centuries and it just has not been found. It is not there. So with the roman and greek eyes, the scriptures are re-interpretated to mean something that is not there. If the scriptures are understood from the Jewish perspective that the jewish writers wrote it in, the true flavor of what is written come forth.