You'll really will need the spanner wrench for the spanner nut on the basket drive block. If you try to make a tool or use some other method, you risk injury and possibly damaging your washer basket.
The spanner wrench is made by Supco, part #TB123A. It has various other part numbers from the appliance manufacturers. It is compatible with Whirlpool, Maytag, GE, and Kenmore. Most Kenmores are made by Whirlpool.
If you want the wrench same day, call local appliance shops and ask if they sell the spanner for the Kenmore Series 90. I got mine from a local shop and paid $13.
You could also buy one on eBay or another reasonable online source.
Or Google search: TB123A
Don't pay more than $20 including shipping.
You can always sell it on eBay once you are done with it. It won't lose much value being used since it doesn't really wear out.
You'll need a hammer too, preferably with a hard rubber head, or use a wooden mallet. If you use a steel hammer, be careful when you strike the spanner wrench to loosen the spanner nut. Wrap the steel hammer head in an old washcloth or rag. You don't want to accidentally strike the porcelain enamel lining of the basket - it will chip and that can lead to rust of the metal.