James, you have stepped off into some very deep water.
First, unless your Sensei has approved your use of a shinken for iaido training, don't even think about using one!! That is unless you plan on counting your fingers every time you draw the blade.... And if he/she has approved your use, why not ask what he/she recommends?
Assuming that you're moving forward here, there are distinct differences between a shinken - a "live blade" that is normally used for tameshigiri, or test cutting - & a Nihonto, which is a traditionally-made blade from a Japanese smith. There are a few of us whose Sensei does require us to use a Nihonto in training, but I know of VERY few of us.
A Nihonto can cost anywhere from a few hundred dollars for something that's mostly rust, all the way up to hundreds of thousands of dollars...& above. A shinken may cost you a few hundred to a few thousand dollars, depending on how you want it to be outfitted. After swinging swords for several decades, I don't see or feel a lot of difference between my light-weight shinken & my light-weight Nihonto for training. That takes into account balance & weight, although I've found that shinken tend to weigh a lot more because they are intended for cutting tatami omote & bamboo.
Hope this clarifies things a bit.
Ken Goldstein
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Judo Kodansha/MJER Iaido Kodansha/Jodo Oku-iri
Fencing Master/NRA Instructor
"A positive attitude may not solve all your problems, but it'll annoy enough people to be worth the effort."