Anything you can do is fine, and using a handheld is MUCH easier than a corded vac. Handhelds might not be as powerful, but every little bit helps.
Have you considered a mattress cover?
If you just use your regular vac on it a couple times over, then put your mattress in an allergy cover, you should be good to go. You can remove the allergy cover for washing, which is a lot easier than trying to clean the mattress. You can get a decent allergy cover for under $50 USD, depending on the size of the bed.