The software that will be making use of is open source
No, it isn't. You said that it has no license. Then it isn't open source. If it has no license that grants you specific rights in addition to the rights given to you by copyright law (which are practically none), then it isn't open source. In particular, you are not allowed to copy it, modify it, distribute it, not even download it, etc. Depending on your jurisdiction, you may not even be allowed to run it since running involves copying from disk to RAM; most jurisdictions have thankfully moved away from this ridiculous interpretation, but there may still be some that haven't.
Am I allowed to use the original unlicensed version without any implications?
You never were allowed to use that version in the first place, and you still aren't allowed to use it now, since its (non-)license hasn't changed a bit.