I assume by "sprouts" you mean alfalfa sprouts bean sprouts or similar.
I have never heard of adding fertilizer to sprouts. I doubt this is needed, and question the safety. If you try it at all, YES, make sure it is VERY dilute!!
Here is a potential risk. Some crops when receiving high nitrogen fertilizer can initially store nitrogen in tissue as nitrate or nitrite, both of which are potentially dangerous (emphasis here on YOUNG plant tissue). This may not be a high danger unless you eat a lot of sprouts, but be aware of the risk, weigh your options. Personally I never add any fertilizer to sprouts, and have had no issues producing sprouts.
You can use your high nitrogen fertilizer elsewhere in the garden on other crops where the crops grow and mature for a while. Plants convert the nitrate-nitrogen into other forms, including protein, as plants grow and mature.
The expiration date probably has more to do with a date past which maximum potency can't be guaranteed. I would use it elsewhere in the garden and not worry abut it too much.
