It is possible to make the formatting methods available without the alloc feature with relatively little changes.

1. Format to fmt::Formatter instead of String. This means replacing push_str() with write_str()?, and replacing push() with write_chr()?.
2. When creating a DelayedFormat the timezone name is rendered to a String. I have replaced this with a fixed-size buffer of 63 bytes. It was slightly tricky to get the Display method of Offset to format into a byte buffer, that is what TzName is for.
3. Display can take some tricky formatting specifiers to justify/pad/truncate our formatting result. This is very difficult to do without rendering the intermediate result to a String. As solution I choose to render to an intermediate string in such a case in Display::fmt, and to ignore the specifiers in no_std.

Part 2 and 3 seem like a small price to pay for making all these methods available to no_std targets.

Previously DelayedFormat gave the impression it would work without allocations (also in the documentation), because 'why else would we have this type'? But the first thing it did was create a temporary string to write into 😆.