With substantial training and practice, a tongueless person can learn to speak again. Intelligibly. Your characters may choose not to do that though.
Also, I frame challenge your assertion that people who are drunk/high enough to have fine motor ability impaired can not use sign language. If you're so impaired that you can't sign at all, then you're unconscious (or close to it).
Remember, signers can slur their words just like speakers do. In fact, speaking requires more fine motor control than signing does. This is why bilingual children learning both a signed and a spoken language will learn the signed one first. And why children with motor impairments are often taught basic sign language.
But to answer your question directly, there are various sounds that one can produce without a tongue.
For consonants, there are 3 basic parameters for every sound:
- Voiced vs unvoiced
Voiced vs unvoiced refers to the involvement of the vocal cords. Put your hand lightly on the front of your throat. Make a long "s" sound. Now make a long "z" sound. Feel the difference? The "z" is voiced; you will feel the throat buzz as the vocal cords engage.
Removing the tongue will not affect voicing.
Placement means where the sound is being made. No tongue greatly restricts the possibility of most consonants because they are made by the tongue (the tip, the middle, the back) in contact with various parts of the mouth.
But several are made without the tongue.
- Labial sounds like "b" and "p" (the first is voiced, the second unvoiced)
- Labial-dental sounds like "v" and "f"
- Some glottal sounds like a glottal stop
Movement is another characteristic of consonants.
- Stops are quick sounds like "b" and "t"
- Fricatives are prolonged sounds like "z" and "sh"
- Liquids are semi-prolonged but where the contact is pretty minimal, like "l"
- Clicks are faster and harder than stops. They are not present in English, though all English-speakers can produce them (super simple versions) as they are used for other forms of communication and play. Again, placement is paramount. Labial clicks won't be impaired.
While the tongue is involved in most of those movements, it really depends on placement. They can also be made with the lips, the lips in conjunction with the teeth, and with the throat.
Vowels are more complex. They all involve the shape and placement of the tongue during voicing. They're prolonged and don't have substantial contact with other parts of the mouth (beyond just fitting in the mouth).
Even without a tongue though, the mouth can change shape. This can approximate many vowel sounds. Enough for basic communication.
Ditto for some of the consonant sounds.
To sum up...and to offer a massive frame challenge.
While your question about the sounds produced without a tongue is straightforward and reasonable, your premise is full of holes. A lot of "sensitive information" is vulnerable to someone who can't do anything but nod "yes" or "no." Drugging someone with "truth serum" or whatever won't stop them from signing or writing. Slurred signing or writing will still give away secrets. And removing the tongue doesn't stop people from speaking to some degree. It would be enough to compromise security in many cases.
While it's true that removing tongues is used in some fiction as a security measure (the Song of Ice and Fire series has a few cases; though these are people who don't know sign language (one is never mentioned as part of the society) and who are illiterate). Even so, they could give a lot away if motivated to. They don't because they're afraid of losing more body parts or their lives.
It's just not as effective as you think it is. You can't take someone fluent in one or more human language, remove their tongue so they don't involuntarily spill secrets during interrogation, teach them a coded spoken language, then expect that only the coded version will come forward if they're too drugged to control what they say. Honestly, I can't even imagine this.