It does sound strange and contrived, but it is perfectly correct. So if it helps you to remember the word, go ahead. It's no stranger than these:
"I know no rules for English spelling."
"If the diagonals are equal, it is a square square."
"What play did the playwright write?"
"I can't glue it together." "So sew it."
"Are you sure this is the right rite?"
I would add, though, that "straight" is a very common word; it is basic vocabulary; it is used all the time. It is important to know how to spell "straight." "Strait" is a rare word. It is mostly used in a geographical context. I am not sure why you want to memorize the word "strait." Also, even though "a straight strait" makes perfect sense, most _geographical_ straits are not straight so it is not something you would say very often!