What makes you suspect that these are re-hilted rapier blades?
Your first one retains the shoulders of the blade, so if it was originally a rapier it would have need to have lost a good portion of it’s tip. Is the blade unusually thick at the tip? If not, it will be a purpose built smallsword blade since the effort in re-profiling a blade from the base will be more work than making a new one.
As an aside, I’m always cautious when mixing Rapier and Smallsword (like so called transitional rapiers). Because rapiers command a premium over smallswords, I find some dealers are quick to find links between the two to add value.
I appreciate that transitional rapiers are a thing, they’re just not as common as some make out to be in my view.
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