The JPS Tanakh version, a Jewish translation of the Masoretic Text, puts it somewhat differently:
If you are loath to serve the LORD, choose this day which ones you are going to serve—the gods that your forefathers served beyond the Euphrates, or those of the Amorites in whose land you are settled; but I and my household will serve the LORD
Another Jewish translation of the Masoretic Text, this by Rabbi A.J. Rosenberg:
And if it displeases you to serve the Lord, choose this day whom you will serve, whether the gods which your fathers served that were on the other side of the river, or the gods of the Amorites, in whose land you dwell, but as for me and my household, we shall serve the Lord
Regarding the theme of choice in this instance, Professor Nili Wazana, Senior Lecturer at the Department of Bible and the Department of Jewish History at the Hebrew University of Jerusalem notes:
The motif of choice is found in international treaties, the vassal depicted as choosing his overlord just as cattle choose their stable (e.g. the treaty between Hatti and Kizzuwatna, ca. 1400 BCE). But I ... will serve the Lord possibly [alludes] to the traditions that God would start a new nation with Moses (Num. 14.12; Deut. 9.14), implying that if all Israel is not obedient, God could start anew with the pios Joshua and his family.1
The Septuagint rendering here is (Brenton translation):
εἰ δὲ μὴ ἀρέσκει ὑμῖν λατρεύειν κυρίῳ, ἕλεσθε ὑμῖν ἑαυτοῖς σήμερον, τίνι λατρεύσητε, εἴτε τοῖς θεοῖς τῶν πατέρων ὑμῶν τοῖς ἐν τῷ πέραν τοῦ ποταμοῦ, εἴτε τοῖς θεοῖς τῶν Αμορραίων, ἐν οἷς ὑμεῖς κατοικεῖτε ἐπὶ τῆς γῆς αὐτῶν, ἐγὼ δὲ καὶ ἡ οἰκία μου λατρεύσομεν κυρίῳ, ὅτι ἅγιός ἐστιν.
But if it seem not good to you to serve the Lord, choose to yourselves this day whom ye will serve, whether the gods of your fathers that were on the other side of the river, or the gods of the Amorites, among whom ye dwell upon their land: but I and my house will serve the Lord, for he is holy.
where Brenton translates ἀρέσκει (from ἀρέσκω - areskō; please or satisfy) as "seems good".
Origen (184-253) put this verse in the context of the catechesis of Christians (a period of instruction undergone by early Christians prior to Baptism):
Therefore, what Joshua said to the people when he settled them in the holy land, the Scripture might also say now to us. The text reads as follows:
Now fear the Lord and worship him in sincerity and righteousness (Joshua 24:14)
And it will tell us, if we are being misled to worship idols, what follows:
Destroy the foreign gods which your fathers worshiped beyond the River and in Egypt, and worship the Lord (Ibid.)
Then in the beginning when you were going to be instructed, it would have been rightly said to you:
And if you be unwilling to worship the Lord, choose this day whom you will worship, whether the gods your fathers worshiped in the region beyond the River, or the gods of the Amorites among whom you dwell on the land.
And the catechist might have said to you:
But as for me and my house, we will worship the Lord because he is holy.
He does not have any reason to say this to you now; for then you said:
Far be it from us that we should forsake the Lord, to serve other gods. For the Lord our God, he is God, who brought us and our fathers out of Egypt … and preserved us in all the way that we went (Joshua 24:16).
Moreover, in the agreements about religion long ago you gave your catechist this answer:
We also will worship the Lord, for he is our God (Joshua 24:18).
If, therefore, the one who breaks agreements with men is outside any truce and alien to safety, what must be said of those who by denying make null and void the agreements they made with God, and who run back to Satan, whom they renounced when they were baptized? Such a person must be told the words spoken by Eli to his sons, If a man sins against a man, then they will pray for him; but if he sins against the Lord, who will pray for him? (1 Kingdoms LXX/1 Samuel 2:25)2
I don't believe there is anything in the Biblical text itself, nor in Jewish or Christian interpretations of the text in antiquity (nor for that matter in modern Jewish or modern eastern Christian interpretations), that suggest that the choice being discussed was something other than free.
1. Oxford Jewish Study Bible (2d. ed.)
2. Exhortation to Martyrdom XVII