No, they don't have to be 34 beads wide. For many patterns you can cut off columns if you want the cuff to be smaller, but realize that the pattern is going to wrap around the cuff more, and make sure that you can get your hand inside the cuff. I've found that below about 26-28, I can't fit my hand inside, even though my wrist is only 23.
At the bottom of this page is a diagram of how you would modify a pattern to be smaller. For some patterns it will require removing the background detail, the double sided-ness, or extra elements, e.g. pokeballs. The patterns that you won't be able to trim without completely reworking the pattern are ones with backgrounds that are designed to match up, e.g. many of the striped ones, or ones where the pattern takes up the entire cuff, such as the Cinnamoroll one.
Example: The pattern below is 36 beads wide. If you wanted to make it 30 beads wide instead, you would cut off the last six columns as shown. Be sure that when you're removing columns, you remove an even amount, e.g. 2, 4, 6. To "cut off" columns, you can either print out the pattern and literally cut them off. Or if you're making it from your computer screen, cover up those columns with another window or edit them out in Paint or another graphics program.