2-pin 15amp cord replaced with 3-pin 15amp?

I just acquired a Luxman CD-player and it turns out the IEC connector on the back is 2-pin (a 2-pin to 2-pin powercord is supplied).  Can I safely use my after-market 3-pin cord on it (JPS Labs digital ac-x)?  The shape of the connector on the back of the unit looks to be identical.  The ground pin will be in the receptacle in the wall, but it won't be going anywhere at the CD-player end.  Does that matter?  Does it remove any benefit derived from using the JPS Labs cord?
Yes, you can use a three pin male plug safely even if the ground is not connected at the other end, and it should perform better than the stock cord - be interesting to see if you hear a difference. Also you were lucky the two pin (C7) outlet styles matched as there are both polarized and non polarized variations of these 😆
Some would argue that the cables performance will be even better with only 2 prongs on the female end. I think the argument is that you still get the ground shielding effect without the possibility of ground loop noise. 
Yes, perfectly safe.

A shielded cable of modest cost will offer benefits.

Never remove a ground when the equipment requires it. 
Thanks all.  Everything installed this morning and working well.