This is my favorite Wii game and to make the game more difficult I sometimes played it without gathering any items. Actually not getting any mushrooms can be a challenge as you have to circumvent getting drawn into the "worlds" where you can get those (i.e. let yourself be killed if you do).
So you can do 9-7 without star item from my notes (not sure if they make sense to you):
With helicopter wait before first green pipe, after being shot at jump up and helicopter high than land on the bottom (not the ledge to the right of the pipe), jump up to the icecubes (one of them is gone), run right, jump and helicopter (all shots will go high). Drop down, run right, helicopter to get coin (shots should go high), drop down, helicopter past. Run right helicopter.
After that you should be around the point where you can get if you use a star item and run without stopping.
Run, jump, wait until you are above the second shooting plant above the long ice bridge. Wait there until enough blocks are melted by the plant to the right so you can get at coin. Run right, crouch/slide and then helicopter and drop down to kill the first of the two turtles, then do the same for the second turtle. Jump down + helicopter to get last coin.
I actually find the last coin of 9-4 more difficult to do than any of the 9-7 coins.