You cannot be that selective, because in Luke 11 the Greek for "sins" is the same Greek as in 1 John 1 and 1 John 3:
Luke 11:2-4
2 And He said unto them, When ye pray, say, Our Father Which art in heaven, Hallowed be Thy name. Thy kingdom come. Thy will be done, as in heaven, so in earth.
3 Give us day by day our daily bread.
4 And forgive us our sins; for we also forgive every one that is indebted to us. And lead us not into temptation; but deliver us from evil.
KJV
1 John 1:8-10
8 If we say that we have no sin, we deceive ourselves, and the truth is not in us.
9 If we confess our sins, He is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.
10 If we say that we have not sinned, we make Him a liar, and His word is not in us.
KJV
The essence of the matter about sin is that it is violation of God's laws, like John said in 1 John 3:4. The Holy Spirit is given us through Christ to help us have God's laws written in our hearts and minds to follow them. This is part of Paul's teaching in Galatians 5 that IF... we walk by The Spirit, then we become dead to the law. If we don't, then we place ourselves back under the law.
Thus John is right, we are still able to transgress the law, call it a slip up, a sin, or whatever you want. Scripture calls it a violation of God's law, even Apostle John did. The difference between those of us in Christ though, is that we are to 'repent' to Jesus when we do slip up, and John says He is faithful and just to forgive us our sins. This is why our Lord Jesus showed us to ask forgiveness of our sins when we pray, as per Luke 11.
In Romans 7, Paul teaches us to assume ourselves as dead to sin, even though it is impossible to fully prevent it from happening, because of our flesh.
Rom 7:14-25
14 For we know that the law is spiritual: but I am carnal, sold under sin.
15 For that which I do I allow not: for what I would, that do I not; but what I hate, that do I.
16 If then I do that which I would not, I consent unto the law that it is good.
17 Now then it is no more I that do it, but sin that dwelleth in me.
18 For I know that in me (that is, in my flesh,) dwelleth no good thing: for to will is present with me; but how to perform that which is good I find not.
19 For the good that I would I do not: but the evil which I would not, that I do.
20 Now if I do that I would not, it is no more I that do it, but sin that dwelleth in me.
21 I find then a law, that, when I would do good, evil is present with me.
22 For I delight in the law of God after the inward man:
23 But I see another law in my members, warring against the law of my mind, and bringing me into captivity to the law of sin which is in my members.
24 O wretched man that I am! who shall deliver me from the body of this death?
25 I thank God through Jesus Christ our Lord. So then with the mind I myself serve the law of God; but with the flesh the law of sin.
KJV
Paul made a simple distinction there between a law that is in our flesh, vs. the law of God after the inward man, or the spiritual. As Paul said in Romans 6:7, he that is dead (in the flesh) is freed from sin.
Thus it's our flesh that causes most of our slip ups today, and that's why we still need to repent to Christ asking forgiveness of those sins when it does happen. That is one of the reasons for Communion with Him also (I don't mean the Catholic system either; we can hold Communion in our own homes).
So how do we reconcile what John said in 1 John 3:9? It simply means those born of God are not habitual sinners like the wicked who love to sin, like those in Isaiah 5:18 that pull a cart rope (i.e., pull a cart full of sins for show & tell, bragging about their sins).