An “outstretched arm” is the sword, as it says “and his sword was unsheathed in hand, outstretched over yerushalayim” (Divrei Hayamim 1 21:16)
Another way of understanding this Drash is that just like the sword threatening Yerushalayim, there was also a ‘sword’ in Egypt threatening the Jewish people with destruction. Moshe told Pharoah at the beginning (Shemot 5:3)“lest God smite us with a plague or the sword” (understanding “us” literally instead of as a euphemism for the Egyptians)). Moshe told Pharoah that if the Jewish people are not allowed to travel 3 days to serve God, they are at risk of being destroyed.
The Jewish people in Egypt had assimilated to the point where the monotheism of Avraham was almost completely forgotten. And the Jewish people had turned to idolatry. There was a good argument (placed by Chazal into the mouths of the angels) that there is no difference between the Jews and Egyptians, and that it is unjust that these are saved while these are destroyed. Thus with Yetziat mitzraim there was an outstanding threat to the Jewish people’s survival. We were in a tenuous position, on the precipice of falling back to Avodah Zarah. Even after the mitzvot of milah and korban pesach, these achievements were fragile and if we would falter our very existence would be at risk.
In fact this almost happened after the Golden Calf. When we were deserving of destruction, and were only saved through Moshe’s Tefillah and leadership. And, just like in the time of King David the solution was the mikdash. David recognized that in order to prevent the error which would lead to our destruction, we needed to recognize the nature of the fantasies which would destroy us, and redirect them into a framework of Avodat Hashem, through the Mikdash. So too, in the aftermath of the golden calf we were directed to build the Mishkan.
Even with the Mishkan we were still in a fragile and vulnerable position. After the accepting the spies slander of the Land of Israel, we were, again, almost destroyed. This fear of destruction was present all the way until we entered Israel. Until we entered Israel, and restored Brit Milah, the success or failure of Yetziat Mitzraim was still unknown. And only then the sword was removed.