Roxas was a sort of anomaly to begin with because of several different factors playing into his initial birth:
1. Sora retaining his identity even as a Heartless which left Roxas with no memories and thus a blank slate which could develop into its own being. When he finally got some of Sora's memories after the whole CoM incident he didn't adapt those as his own (as i.e. Axel adopted Lea's memories or Saix Isa's).
2. Kairi restoring Sora's humanity leading to the special occasion of Nobody and Original existing at the same time and Sora retaining his memories for good (until Naminé messed them up in CoM).
3. Ventus' heart being in Roxas which not only affected his appearance, but also helped accelerate the development of Roxas' own heart alongside his connection to Sora.
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If we now hypothesize that current (read: End of KH III) Sora would lose his heart the third extra factor Ven's heart is definitely out of the equation as Ven is back in his own body, despite if their close heart connection might remain.
If Sora would retain his identity as a Heartless again just like the first time around, it would mean any new Nobody would be born a blank slate just like Roxas was, but without Ven's heart in the mix that Nobody would look just like Sora.
In KH 1 Sora does say that while being a Heartless he did start to forget so that indicates that with some delay Sora's memories would eventually start to transfer to his new Nobody if Kairi (or someone else) isn't there to restore him in a reasonably quick time.
So how a hypothetical second Nobody would turn out would depend on how factors 1 and 2 play or not play out this time around as factor 3 is definitely out.
If neither factor 1 and 2 apply then the new Nobody would be just like Lea/Axel, Ienzo/Zexion and Isa/Saix etc. The body with all of Sora's memories while his heart would be a normal Heartless.
If factor 1 applies but not 2 then the new Nobody would be a blank slate for a short time until Heartless Sora starts to forget after all and the memories slowly transfer to the Nobody. Main issue here is how long the memory transfer takes as the longer the Nobody is around without Sora's memories, the bigger the chance being him starting to develop an own identity, and if he has contact with other hearts during that time, even developing his own heart.
If factor 1 does not apply it means Sora will be a normal Heartless so it is questionable if factor 2 can even be applied if factor 1 cannot. If Sora is a normal, read: aggressive, instinct driven, Heartless, can Kairi even single him out to restore him?
If she could do this regardless, we would however have a totally amnesiac Sora because all his memories are with his new Nobody.
If both factor 1 and 2 apply though we have roughly the same situation as we already had with Roxas, the differences being that Sora's second Nobody would not look like Ven and not have his heart as a booster to develop his own heart faster.