How can a person do Teshuva Shabbos without saying vidui?
Teshuva by definition means to return and come close to Hashem. There are many ways to do this, such as thinking aboiut Hashem, doing what Hashem wants us to do, etc. these are all included in teshuva. It is definitely permitted to do these things and a mitzva to do such things on Shabbos. Although we don’t say vidui on Rosh Hashana, it is still the first two days of Aseres Yimei Teshuva! This is because thinking that Hashem is the king and doing His will are all part of teshuva.