Should the expression be romanized as "shele-yad"  or "she-leyad" ?

The answer depends on whether the constituent expression is "le-yad" or "leyad."  *That* depends on how it is entered in       Even-Shoshan's dictionary, as prescribed in HCM, p. 21. 

In that dictionary, "leyad" is entered under "L" but is also discussed under "yad,"  and so, per HCM, "the more 'analytical' option is chosen"-- in this case, "le-yad.": adding "she-" to "le-yad" yields "shele-yad."