Well...katana is the "live blade" equivalent to the bokken, but the training behind it is different from the bokken work done in Aikido. Not only that, the specs for the katana would vary from person to person, and would also depend on the sword style being studied.
Well, Aikiken isn't swordsmanship, per se, and I've only ever seen it done with bokuto. I've heard of there being some kind of Aiki Batto, but never seen it, so I don't know if they use Shinken or Iaito. What does your sensei say?
Personally I have never (12+yrs) used ANY live blade in my Aikido practice. Yeah bokken plenty but for me the use of the bokken is not a training utility for any eventual use of a live weapon but rather once you become more familiar with the extension of your ki through the unbendable arm you will appreciate that the bokken is simply an interpretation of the use of this energy... anyway that is my opinion and your school may certainly train with live blades but it is a thing I have not heard of within my own Aikido circles
If your interest veers more towards bladework then I might suggest popping into your nearest Iaido dojo to see how they do it.. the techniques may look similar to the bokken kata in your Aikido but the intent and direction is a polar opposite.
In my dojo we do not train with live blades, but I have an interest in swords and if I was every to buy one, I'd want to buy one which was suited to the Aikido bokken katas, if there is such a sword.
I wouldn't for example buy a Kung Fu sword because I have no background in Kung Fu.
Every blade we train is live-every blade we use are philippino as ther are combat ready for every posable cut-angle-thrust-rake-twist.I enjoy the samari swords & love the ballance-these I keep locked up.They are more espensive & great craftmanship on the scaboards & tangs.
IF you want to do whatever you do in Aikido but with a "liver" blade than a bokken, and have made up your mind to buying a sword whatever we might say , buy an unsharpened iaito. It keeps your body parts attached where they should be, and is way safer than cool wallhangers. And remember, you won't be able to do paired kata with this!
In this case a visit to an iai dojo would still be necessary, as buying an iaito isn't "easy" if you've never trained with one (choosing length, weight, tsuba form, where to buy etc.). Way different from buying a bokken. And I'd still recommend joining an iai class to learn how to use the thing.