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Specifically, would a creationist say that after regeneration a newly created nature exists, and would a traducianist say the old nature is merely re-shaped.
If we took Delitzsch’s statement “the continued creation of souls is inconsistent with God’s relation to the world,” and applied it to regeneration we see that God is so transcendent that He no longer works in the world. Thus, man would be left to make his own way in salvation with a little help of one named Jesus on the Cross (a crude way of describing Arminianism). Delitzsch would most certainly be agast at this.... God is immanent, near, or presently at work in this world. God did not just create once and leave. He is immanent all the way through the OT. Then came the glory and promise of the Cross and then the majesty and working of Holy Spirit. God is presently at work. The proper view of Christianity is that God is both transcendent and immanent—there must be a balance in our perception here ….

Scripture says we are "new creatures" or "creations." I think Jesus said it well in:

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John 3:3-7 Jesus answered and said unto him, Verily, verily, I say unto thee, Except one be born anew, he cannot see the kingdom of God. Nicodemus saith unto him, How can a man be born when he is old? can he enter a second time into his mother's womb, and be born? Jesus answered, Verily, verily, I say unto thee, Except one be born of water and the Spirit, he cannot enter into the kingdom of God! That which is born of the flesh is flesh; and that which is born of the Spirit is spirit. Marvel not that I said unto thee, Ye must be born anew.
As seen above Nicodemus asked Jesus if the new birth could be after traducianism (can he enter a second time into his mother's womb, and be born?) and Jesus answered, "No," the birth must be after creationism because “That which is born of the flesh is flesh; and that which is born of the Spirit is spirit. Marvel not that I said unto thee, Ye must be born anew.” Ok, I am just having some fun here, however, while this does not prove creationism it does in fact stress: (1) the new creation as opposed to a re-creation (2) it shows God presently at work and (3) since God is a Spirit (as seen in the next chapter, John 4:24) those born again are born of God. The soul comes from God and is not generated by man. As Paul says in 2 Cor 5:17, “Wherefore if any man is in Christ, he is a new creature: the old things are passed away; behold, they are become new.” However, he adds in verse 18, “And all things are from God.” No one can ever say that being born again has its origin in human beings, for Paul clearly teaches that God is the originator and source of this birth. God created all things through Christ Jesus (John 1:3; Col. 1:15–18; Heb. 1:2)…..

Reformed and Always Reforming,