The day 21 test is used to test for progesterone, which is a hormone only produced after ovulation, and therefore this test should be carried out seven days before your period. If your periods are irregular, the sample might be taken on the wrong day, although three days either way will not matter, and if a sample is taken on the same day each week, one of these is bound to be about a week before your period.
A better way to time this sample is, as you suggest, by testing for the LH surge and then taking the sample for progesterone seven days later. If you were to ovulate in one of your shorter 40-day cycles, your blood progesterone concentration would not start to rise until the day of ovulation, which would be about day 26. The value would be maximal at about day 33, which is when the blood test should be taken. I would suggest you also have a blood sample taken on day 39, just in case you have a 46-day cycle.