Sometimes a spider will graciously extend its palp for you, but especially with small spiders you may have to help the process along. Applying pressure to the palp patella area with a wire is usually enough. I always slide it under the plastic or first layer of tissue paper rather than directly touching the spider so there's no risk of accidentally poking it.

This doesn't always work right away. You might need to try it a couple of times. If the spider is really stubborn, giving it a bit more room by raising the restraint slightly may help encourage it to stretch out. Then you can get the wire underneath. Once it's in place, chances are the spider won't have enough space to pull the palp back.