If one will not have 3 people with him, can he say the moser modah privately to himself?
Yes he can say it privately, although it is better to say it in front of 2 or 3 people. It is also preferred that it be said and not just whispered.
Ran Nedarin 23a, Rosh Ibid 4, Y:D 311-1, Halicho Shlomo 2 Ku8ntris Shalmei Nidarim 15 ftnt. 15, Kol NIdrei 81-9,10.