As we all know, hydrogels are basically polymers having viscoelastic properties, I was confused in the selection of strain rate while performing tensile test.
Choosing a strain rate is highly dependent on what you are trying to learn from your hydrogel. Typically the strain is kept low as hydrogels are fragile and small strains can result in your material leaving the linear viscoelastic range. To ensure testing is nondestructive an amplitude sweep with strains in the range of, roughly, 0.01% to 100% is done first.
I reiterate Dalton comment, it really depends on what you would like to learn about mechanical behavior of your hydrogel, then you will decide on conducting tensile test or rheology. It also depends on the stiffness range of your hydrogel. If stiffness is less than ~500 Pa, it is unlikely that you can perform tensile testing.