I think you still have stealth - just active instead of passive.
Snake's stealth was more of a "waiting stealth".
Raiden's stealth, I believe, was called "hunting stealth".
ETA:
The character you control in Rising, Raiden, is almost the total opposite of usual MGS protagonist Snake and his style of stealth will be quite different. Raiden is a very acrobatic ninja. While Snake would wait patiently for an enemy to walk by, Raiden won't be standing around twiddling his thumbs. He can move undetected and easily sneak up on enemies while remaining in stealth mode. Konami calls this "hunting stealth."