A.T. Robertson Commentary 2 Corinthians 10:2

"yea, I beseech you, that I may not when present show courage with the confidence wherewith I count to be bold against some, who count of us as if we walked according to the flesh." — 2 Corinthians 10:2 (ASV)

I beseech (δεομα). So here, but παρακαλω in verse 1. Perhaps, "I beg" suits the new turn here.

That I may not when present show courage (το μη παρων θαρρησα). Articular infinitive (aorist active of θαρρεω) in the accusative case with negative μη the direct object of δεομα. Literally, "I beg the not when present (παρων nominative present participle agreeing with subject of θαρρω in spite of being in the accusative infinitive clause, το μη θαρρησα) showing courage." The example of humility in Christ makes Paul drop "from magisterial exhortation to earnest entreaty" (Plummer).

As if we walked according to the flesh (ως κατα σαρκα περιπατουντας). Another sneering charge as made plain by the use of ως with the participle for the alleged reason.