Shami was drafted into the side at the Hampshire Bowl last weekend in place of the injured Bhuvneshwar Kumar and took four for 40, including a final-over hat-trick which extinguished any hope of a monumental upset.
Bhuvneshwar is back in contention following a tight hamstring ahead of Thursday's meeting with the West Indies at Old Trafford, where India could all but secure a semi-final place with a win.
But Arun was giving little away as to who India would select from Bhuvneshwar and Shami, merely pointing out they are happy with the options at their disposal.
Arun said: "Bhuvneshwar's injury is not of any great concern. It is just a niggle, which we didn't want to take a chance with. And it was also an opportunity for us to plug Shami into the games.
"But the fact he's done exceptionally well all goes well for us; it's an embarrassment of riches.
"We would take a call as per the conditions, but Bhuvi has done exceptionally well, so I think it's a pretty good headache to have."
Shami's fortunes contrast sharply with 12 months ago, when he was dropped from the side ahead of a Test against Afghanistan after failing a fitness test amid personal issues away from the game.
Arun added: "Shami was in a totally different mindset (a year ago).
"The head coach, me, all of us had to sit down and speak to him and kind of draw a future map for him and had to convince him regarding that. And he was going through certain personal problems as well at that point in time.
"Beyond all that, I think what has really got him into the situation that he is in his ability to play cricket and that's exactly what we made him focus on. And I think the rest is there for everybody to see."
The Windies have a number of batsmen, led by Chris Gayle, who are capable of routinely clearing the boundary rope, but that holds no fear for India's bowlers, according to Arun.
He added: "They do have their strengths. And also it's a big challenge for the bowlers too, especially when they come after you.
"But whenever batsmen come after you, if you're willing to look at it deeply, there is a chance for the bowlers, and I think that's what the bowlers would be looking to do."
