The halacha is that one must stand while saying viduy (S.A. 607:3.) Why must viduy we recited while standing? The Mishne Berurah explains that standing demonstrates greater sense of subservience and will establish a better confession. The Kaf Hachaim quotes the Yafe L'lev that is based upon the possuk in Nechemya (9:2) ויעמדו ויתודו על חטאתיהם וכו. The Mishne Berurah cites the Pri Migadim is unsure is this law of standing is מעכב.
The Magen Avraham says one must be carful not to lean on something that if it is moved, the person will fall for that is considered sitting not standing. Rav Wahrman develops based upon various sources an idea that this rule only applies when standing is required innately but if one stands only for honorific purposes or for other external factors, then even when standing by being propped up, sine it still appears as if one is standing, it suffices. With this difference, he suggests according to the reason of the Mishne Berurah ,it should suffice with leaning for the standing f viduy (this would be not like the Mishne Berurah who quotes the Magen Avraham here that holds it does not work.) With this he answers the question of the Emrei Emes of how can one do viduy on a korban while doing סמיכה if one is leaning on the animal and the person will fall if it is removed? According to this, this suffices for the standing of viduy.
Another answer Rav Wahram suggests is to differentiate between the types of viduy. Viduy as part of teshuva requires standing but the viduy on a korban is not part of the teshuva process, it is a viduy that it is a halacha in the korban. Part of bringing the korban is to say why one is bringing the korban and that entails a viduy but that viduy does not require standing.
A third approach to the requirement of standing during viduy is suggested by Rav Yerucham Olshin. He suggests that the Rambam stresses many times in the Laws of Teshuva starting with the lists of mitzvot on the top that teshuva is done לפני ה. He says that this law of לפני ה requires standing in the same way as one stands during the amidah for being present לפני ה. (With this it is also understood why the viduy on Yom Kippur is incorporated into the Shemoneh Esrei for they are the same yesod.) With this he suggests that the Rambam does not mention the requirement of standing while doing viduy (which the Pri Migadim points out) because it is already included in the Rambam's words that teshuva is לפני ה.
The Mishne Berurah (620:2) says that one must day viduy ten times within the prayers of Yom Kippur corresponding to the ten times the Kohan Gadol mentions Hashem's name on Yom Kippur. In the Shaar Hatzion he adds that the viduy after maariv doesn't count since it is not part of the Shemone Esrai. It is clear from the M.B. that the viduy of Yom Kippur must be said within the context of prayer. Why? Presumably because of this law of teshuva being said לפני ה. But then this law should always apply not just on Yom Kippur? Rav Yehoshua Eichenstein explains based upon R' Yona that Yom Kippur has a unique mitzvah of teshuva based upon the possuk לפני ה תטהרו and it is that mode of teshuva that requires it be said in prayer. (In other words, regular teshuva according to R' Yona is not לפני ה, it is a maaseh mitzvah like any other but the Rambam vies all viduy as an act of repairing the broken relationship with G-d and hence one must come before G-d to ask for forgiveness.) However, the Rambam holds all teshuva is לפני ה yet doesn't have to be done in tefillah so why is Yom Kippur different? As mentioned in 'Obtaining Tahara' from Rav Solevetchik, the viduy of Yom Kippur accomplishes more than a regular viduy, it accomplishes a level of taharah. Says Rav Eichenstein, Rabbenu Yonah says ועוד יתפלל בעל התשובה אל השם. למחות כעב פשעיו וכענן חטאתיו. ושיחפוץ בו וירצהו ויעתר לו כאשר אם לא חטא, to obtain taharah one has to pray. Therefore, since the viduy of Yom Kippur is to obtain taharah it goes together with the prayer which effects taharah.