Is this a known procedure that you got somewhere? If so, what solvent did they use? In any case, the procedure does seem strange as NaBH4 will no longer be NaBH4 if it touches water (do not even try). Just think about what the products are for NaBH4 + H2O. I doubt any protic solvent would be okay (ie, MeOH, etc.). You'd likely need non-protic, anhydrous solvent which also may create issues for proline solubility.
Don't worry about handling NaBH4 solid in air. What you need to be careful about it what solution you add it to. Also, 200 uL of 333 mM NaBH4 is not a lot. Large quantities may require extra precautions however (again, think of the products that might form/heat that might generate). Be sure to use dry solvent. Also, NaN3 is potentially explosive IMO, but I wouldn't worry about small quantities.
Good luck and be safe!