Hopefully I have interpreted the OP correctly. Conversion from a 7 speed to a 9 speed wheel/cassette will require more than just putting the wheel in place.

1. The space between cogs in the cassette becomes smaller as the number of cogs/speeds increases. 7 speed spacing does not equal 9 speed.

2. The indexed shifter controls the amount the derailleur moves with each detent/click/speed. You must use a 9 speed shifter with a 9 speed cassette. Much of the time, the brand of shifter and the brand of derailleur must be compatible. Many brands such as microshift and sunrace are built to be compatible with Shimano. Suntour, SRAM and Campagnolo mostly don't work with shimano derailleurs. An inexpensive alternative would be to use a friction shifter but if you have never used friction you may find it frustrating.

3. The 9 speed wheel is built to fit in drop outs that are spaced 130(road) or 135(mountain) mm apart. This is called the OLD (Over Locknut Dimension). The OLD of your bike could be 126 mm. If the frame is steel the drop outs could be spread (cold set) to the wider dimension. If the frame is aluminum or carbon fiber you are out of luck.

4. Many people use derailleurs originally sold in fewer speed drivetrains with 9 speed cassettes and shifters. I have used a 7 speed shimano derailleur with a 9 speed sunrace shifter and cassette and it worked perfectly. That does not say that your current 7 speed derailleur will work with the specific 9 speed cassette you have. Your derailleur may not have the capacity to accommodate the largest cog of the cassette. It also may not have the take up capacity to handle the difference between the small-small and big-big combinations of the new drive train. Capacities would only be a concern if the new cassette has much larger cogs. For example, if the 7 speed cassette is an 11-28 and the 9 speed is an 11-34.

5. The outside width of the chain becomes less as the cassette spacing decreases. A thicker 7 speed chain will not work with a narrower 9 speed cassette.

6. SheldonBrown.com is a terrific source for all your questions. You may want to study it a little before proceeding.

It appears to me that if you go ahead with the 9 speed wheel/cassette you will probably need to cold set the frame, obtain a nine speed rear shifter (shimano, microshift, sunrace) and obtain a 9 speed chain. You could also need a different derailleur. After assembly, adjustments will be needed to make it work correctly.

I hope this is not too confusing and helps a little. Remember SheldonBrown.com. Good luck with the project.