You can get an inexpensive digital VOM for about $20.00 at any big box store like Menards, Lowes, or Home Depot. Just be sure that you get one that will measure down to 1 ohm or less. Look for one with a lowest resistance scale that is 20 ohms or 40 ohms. The meter will then resolve down to 1 ohm. This will permit you to measure Re of a 4 ohm speaker accurately. Buying a digital VOM is a good idea. It is a useful device to have in your toolbox, almost as useful as a Phillips #2 screwdriver. You will find many things to do with it, such as checking to see if a wall outlet works without sticking your fingers in it.
To determine if your cart is bad, measure between left cartridge pin, marked with white, and left ground pin, marked with blue. Typically, it will measure between about 500 ohms and about 900 ohms. Then measure between right cartridge pin, marked with red, and right ground pin, marked with green. It should measure the same as the left side. If you have a side that does not measure, or measures a dead short, the cart is not worth investing in a stylus for it. There are a few cartridges that measure in the 1300 ohm range, such as some Shure V-15s, but most come in where I have suggested.
And good luck from the old outlet measurer,