You're right. The Saints did indeed trade a first round pick for Walsh (that should have been obvious since Walsh was himself a first round supplemental pick for which the Cowboys gave up their first round pick in the 1990 draft -- how in the world did I overlook that!!).
The Cowboys then traded that 1991 first round pick to New England:
The Pats traded their 1991 first round pick (#17-Bobby Wilson) and a 1991 fourth round pick (#110-Kevin Harris) to the Cowboys for their 1991 first round pick (#14-Leonard Russell) on 4-21-1991.
The Saints also traded a third round pick in the 1991 draft to the Cowboys and we used that to select Erik Williams.
Finally, the Saints traded a 1992 second round pick (#52) to the Cowboys; we traded that pick to the Browns in a multi-choice deal:
Browns traded their 1992 second round pick (#36-Jimmy Smith) and their 1992 fifth round pick (#121-Rod Milstead) to the Cowboys for their 1992 second round pick (#52-Patrick Rowe), a 1992 third round pick (#78-Gerald Dixon), a 1992 sixth round pick (#163-George Williams), a 1992 eighth round pick (#222-Mike Pawlawski), and a 1992 twelfth round pick (#329-Tim Simpson) on 4-25-1992.
So my response was WAY off; in terms of the three draft choices we got from the Saints, we used only one of them directly to select Erick Williams; the others were packaged with players and draft picks in other deals.
Thanx for keeping me honest!