If you truly want at least the appearance of only one card in play the whole time, most commonly you'll find methods that use verbal, psychological, or both means.
There are thousands upon thousands of scripts and structures out there that use these. Since these methods are gimmickless and sleightless they rely on the human brain, and since the brain is endlessly complex the methods are endless too.
Peter Turner is a big fan of psychological forces, and outlines them in a lot of his work - some of his volumes are dedicated to teaching you how to psychologically force any number or card in a deck. Kenton Knepper also outlines many similar effects in his Wonder Words series, which includes some of the most influential ideas on the use of words and suggestion in modern mentalism. One of these effects, called Truly Invisible, he includes in the Kolossal Killer manuscript (original one only). It requires good participant selection and you'll have to take the card out in the middle of the effect instead of the end, but it's equally powerful.
In the follow up manuscript, Killer Konceptions, Knepper takes the amazing use of the Kolossal Killer as a practical out and applies it to many psychological and verbal forces which on their own, many people would be too scared to use them because of the chance of failure (which becomes smaller and smaller with practice) but now have a safety net with the Killer. The effects and subtleties are incredible, however they are intended for mentalists and so magicians might not feel comfortable with them. They also only graze the surface of the psychology behind them.
You don't have to go gimmick and sleightless though. There are some gimmicks that can help make these methods cleaner/smoother such as the Invisible Card here on T11, sleights such as Shin Lim's The Switch, and endless containers like the Toibox system and David Regal's Clarity Box which can work with sleights to accomplish this effect.
Finally, the ability to pull the exact card you need from your pocket is invaluable - it can be incorporated into all the methods mentioned above. A reference for this can be found in step 4 of 13 Steps to Mentalism.
Hope that helps!
