I’m a relative beginner, but I’m not aware of any work-around if you don’t have a key.
FWIW, here’s what Saunder’s Recorders has to say about it:
It is very common for tenor, and larger, recorders to have one or two keys fitted to the foot joint. (For simplicity I refer to these keys as “C” and “C#”, for F recorders make the mental jump to “F” and “F#”.) There are versions of wooden treble recorders with keyed foot joints. I do not advise these except in cases of physical abnormality or very small (typically a child’s) hands. I am not aware of any plastic treble recorders fitted with keys. When there are two keys they are often spoken of as “split” or “double”. On the tenor recorder one key covers the lowest hole to enable the production of C. If there is no other hole or key low C# is impossible to play. A second key may cover a second hole or control a small hole in middle of the C pad. The systems vary, on some instruments the action of the keys is logical, both for C and one only for C#, and on others, the opposite, one for C and both for C#. You have to know your own instrument.
If you have no C# key you have no low C#. Don’t hold this against your instrument, it matters very little, C# is generally avoided in real recorder music. You can usually find a convincing solution like missing the note out altogether or playing the third above. The C# key, like double holes, is a relatively recent feature.