For conversion too, circumcising oneself is acceptable. Avodah Zarah 10b:
There was once a Caesar who hated the Jews. One day he said to the prominent members of the government. 'If one has a wart on his foot, shall he cut it away and live [in comfort] or leave it on and suffer discomfort?' To which they replied: 'He should cut it away and live in comfort'. Then Keti'ah b. Shalom addressed them thus: 'In the first place, you cannot do away with all of them, for it is written, For I have spread you abroad as the four winds of the heaven. Now, what does this verse indicate? Were it to mean that [Israel] was to be scattered to the four corners of the world, then instead of saying, as the four winds, the verse would have said, to the four winds? It can only mean that just as the world cannot exist without winds, so the world cannot exist without Israel. And what is more, your kingdom will be called a crippled kingdom.' To this the king replied: 'You have spoken very well; however, he who contradicts the king is to be cast into a circular furnace'. On his being held and led away, a Roman matron said of him: 'Pity the ship that sails [towards the harbor] without paying the tax'. [Rashi: Woe to you, since you are laying down your life for their sake, but haven't circumcised yourself, and aren't taking a portion with them.] Then, throwing himself on his foreskin he cut it away exclaiming: 'Thou hast paid the tax thou wilt pass and enter [paradise]'. As he was being cast [into the furnace] he said: 'All my possessions [are to go to] R. Akiba and his friends'. This, R. Akiba interpreted according to the verse, And it shall be unto Aaron and his sons [which is taken to mean that] one half is Aaron's and one half his sons'. A bath-kol then exclaimed: 'Keti'ah b. Shalom is destined for [eternal] life in the world to come!' Rabbi [on hearing of it] wept saying: 'One may acquire eternity in a single hour, another may acquire it after many years!'