halacha - Time for t'filah and you don't have a siddur: better to daven from memory or wait (and possibly miss the time)?

If the set time comes to daven (on a weekday, let's say) and you unexpectedly don't have a suitable (or any) siddur,¹ does halacha call for you to wait (and possibly miss that amidah entirely), or should you do your best without a siddur but at the proper time? Assume that you are not 100% confident that you will do a word-for-word correct t'filah without the siddur, but you think you can get pretty close and are confident that you won't say anything inappropriate.

Is the answer different for men and women, and is there anything else on which it depends?

I wonder if it's ok to daven sans siddur for three reasons. First, if you daven regularly you may find that you've memorized a regular weekday mincha or ma'ariv anyway. Second, the fixed siddur text is only about a thousand years old and before that (as I understand it) only the outline and the chatimot were fixed; if it was at one time permitted to have that level of textual variation, maybe it still is under some conditions. Third, two or three times I have seen an Orthodox Jewish man do this.

¹ Say you don't normally carry a siddur to work because you go to a mincha/ma'ariv minyan on your way home, but something came up and you will miss that minyan on a particular day.