‘For though I should glory somewhat abundantly concerning our authority (which the Lord gave for building you up, and not for casting you down), I shall not be put to shame, that I may not seem (or ‘lest I should seem') as if I would terrify you by my letters.'
In this sentence fitting in the last clause is the difficulty. One way of seeing this is that he is saying that he could, if he wished, glory somewhat abundantly in the authority given to him by God and the Apostles (Acts 9:15-16; Acts 13:2; Galatians 2:7-9) and use it to terrify them by written Apostolic edicts and threats. But that as that authority and power was given to him for building them up, not for ‘casting them down', for positive reasons not for negative, he will not do it. He will not so bring shame on himself. Indeed it his opponents who are the ones who seek to cast them down, not him.
For he does not want to have to use his weapons, as described in 2 Corinthians 10:4, against them as such, only against his opponents. So he will not exert his full authority against them. He seeks only to build them up. Besides their downfall would only result in the discrediting of himself (because he will be seen to have failed)
A second way is to see it as meaning that he is declaring, ‘even though I glory, and even more (somewhat abundantly), about our authority, which the Lord gave for your upbuilding not your downfall, I will not be put to shame' (because I will be successful in that upbuilding because of that authority). The consequence will be that he will not need to be seen as terrifying them with letters, in the way that his opponents accuse him of (2 Corinthians 10:10).
Either way he has no intention of acting in such a way that he will be ‘put to shame' (discredited) by the consequences of his actions, or of doing anything of which he will later be ashamed.