Uncircumcised lips does not imply a speech impediment. When a child is circumcised in the foreskin of the penis, it does not mean that there was a physical disability in the penis, which we have restored. Circumcision is a metonymy for consecration, sanctification, clean. Uncircumcision is a metonymy for unclean, like Gentile pagans, dirty. Thus, the translations which render it as speech impediment, are childish in their understanding of basic figure of speech.
The sense in which the word is used clearly shows that Moses is afraid and deems himself unworthy to speak to Pharaoh, who is a God. It has the same meaning as Isaiah 6:5 where he calls himself unworthy to see and speak to God, for having unclean lips ἀκάθαρτα χείλη. Not because Moses and Isaiah were really unclean, filthy like the Gentiles, but because they deemed themselves unworthy in fear.
Moses, a man of unclean lips: After seeing the vision of the throne of God and the glory of God and seeing the Lord high and lifted up upon a throne, Isaiah said, “… Woe is me! for I am undone; because I am a man of unclean lips, and I dwell in the midst of a people of unclean lips: for mine eyes have seen the King, the LORD of hosts.” (Isaiah 6:4) Isaiah did not try to make any excuses, he did not try to look better than he was, he did not try to reason out what he was seeing. Isaiah admitted that he was a man of unclean lips and that his people were as well and that he had no right to be standing and looking upon the glory and righteousness, holiness, and majesty of the Lord of hosts. Isaiah humbled himself and confessed before God that he was a sinner and undone and unclean.
There were other times in the Bible that people had an encounter with God and felt themselves unworthy and unable to speak. After one encounter with God, Moses declared that he was a man “of uncircumcised lips?” (See Exodus 6:12) When Jeremiah had an encounter with God, he said, “Ah, Lord GOD! behold, I cannot speak: for I am a child.” (See Jeremiah 1:6) When the Israelites had an encounter with God at Mt. Sinai, “they said unto Moses, Speak thou with us, and we will hear: but let not God speak with us, lest we die.” (See Exodus 20:19)
For each of these people mentioned above, God had a solution. For the Israelites, God allowed Moses to be their go-between and speak to God and carry God’s message to them. When God appeared to Moses at the burning bush, He said, “…I will be with thy mouth, and teach thee what thou shalt say.” (Exodus 4:12) Later, when Moses and Aaron stood before Pharaoh, God said to Moses, “Thou shalt speak all that I command thee: and Aaron thy brother shall speak unto Pharaoh…” (Exodus 7:2) The Lord said to Jeremiah, “…Say not, I am a child: for thou shalt go to all that I shall send thee, and whatsoever I command thee thou shalt speak.” (Jeremiah 1:7) Moses, Aaron, and Jeremiah were all of unclean lips and felt inadequate to do God’s work. However, God put His words in their mouths so that they could speak with confidence because the message was from Him.
The sages translated the uncircumcised lips as ἄλογός in LXX Exodus 6:12, which means a-logos- illogical, unreasonable as animals. The uncircumcised Gentiles were also viewed as dirty, filthy, sinners as to be irrational and unreasonable animals. For this reason the NT also used the word ἄλογός in the same context, as brute irrational animals/pagans.
Jude 1:10 (ESV)
But these people blaspheme all that they do not understand, and they are destroyed by all that they, like ἄλογα unreasoning animals, understand instinctively.
2 Peter 2:12 (ESV)
But these, like ἄλογα irrational animals, creatures of instinct, born to be caught and destroyed, blaspheming about matters of which they are ignorant, will also be destroyed in their destruction,
By abusing himself as an unclean man, Moses is merely showing his fear and lack of confidence in facing the Pharaoh.