[Shinken]

I can't speak for replicas cuz i don't have or want any, i can only speak for Iaito and Shinken. But you said that you wanted one that can cut, so that leaves us with just shinken (shinken means real sword) And i guess you can't afford a real handmade? they can be very expencive minimum price is about 600$.
But you can always look at paul chen or hanwei who claims to make handmade sword (thou it is not) They have some swords with a live blade to some affordable prices. And yes most off their swords has a full tang. Of course i don't own any of their sword myself, but i have friends that do.