The correct interpretation here is “out of a straight stick” since an arrow must be straight in order to be effective in shooting. The alternative strait (meaning ‘narrow’) is theoretically possible if one interprets a narrow stick as a thin stick: if an arrow is too thick, it would be too heavy to shoot. Historically, the Oxford English Dictionary lists a few cases where strait meant ‘having little breadth or width’, but all of the citations date from between 1391 and 1527 (see definition 4 under strait in the OED). The scribal spellings for straight and strait in the Book of Mormon manuscripts provide no help in determining the correct word since in the manuscripts both straight and strait are virtually always spelled identically (as strait), no matter what the meaning. See the discussion under 1 Nephi 8:20; also see strait in volume 3.
Summary: Maintain the spelling straight in 1 Nephi 16:23 (“a straight stick”) since an effective arrow cannot be crooked or bent.