The risk of acquiring an STI from unprotected handjob is extremely low. There is no contact with blood and body fluids so there is no risk of infections like HIV, chlamydia or gonorrhoea.
If the person has viral warts or herpes viral infection of her hand, there is possibility of these to be spread by contact. However, the risk is generally low. Viral warts will present with warty bumps on the penis and herpes presents with redness and painful blisters. In the absence of these signs and symptoms, it should be fine.
For this encounter, no specific blood test is required. However, if you have any past history of unprotected sex and want to be certain that you are clear of STI you can do blood test to screen for HIV, syphilis and Hepatitis B.