"Staccato" literally means "separated," not "short."

Personally, I would add the staccato markings if you want the notes separated. Good string players will probably interpret them the way you intend, but it is better to be safe and remove all doubt.

given that the eighth notes are so short anyway(tempo is quarter note = 138 BPM)

"Staccato" literally means "separated," not "short." A staccato eighth note at 138 BPM will still need to be shorter than a regular eighth note at 138 BPM - what matters is the separation of the notes, not the actual duration of the pitch.

Personally, I would add the staccato markings if you want the notes separated. Good string players will probably interpret them the way you intend, but it is better to be safe and remove all doubt.