You will be taking bus or cable carrier from Tatyana station to sinano omachi. So you will not walk for all the way to omachi.
While you are in ice wall, you will have time to walk a little but most of the time you are required to be in any kinds of transportation for your safety.
I have called to one of the hotel near sight seeing area and asked.
According to the lady in hotel near Tateyama Kurobe Alpine route, nobody walk the whole way to omachi because of safety reason. Only some sightseeing area, you will walk. So you just need some waterproof shoes like rain shoes or on-slippery shoes. The lady told me that you should not wear leather shoes.
The clothing, because the area is mostly covered with snow or ice, you better have enough jacket to take on and take off. It is very important to be able to change because you might have to walk a while.
The lady said you do not need to prepare for trekking equipment but better to prepare the cloth to be able to move easily.
http://find-travel.jp/article/2345
Here is the link about the ice walk. You will see some people how they dress.
And if you would like to rent our trekking shoes, (I guess it is not necessary but in case you would like to)
We can send it to hotel you stay.
For returning, you can ask at the hotel you will stay. Even if you do not stay there, you can ask to send from most of hotel in Japan. Or 24hours shop. So you will have no worry to return because we also include Japanese instruction. Once any Japanese see the instruction, they know what to do. The instruction include our number, so they can call us if they need to.