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Something like this?
cal 8 2010 |
awk 'NR<3{next} {
if(NF==1){
next;print $1;exit
}
if(NF<7){
print $1;exit
}
print $2;exit
}'

Or shorter:
cal 8 2010 | awk 'NR>2 &&...

If you are using ksh93 (Korn Shell 93) the solution is trivial

fwdom()
{
# add error checking for $1 $2 (month, year)
day=1
dow=$(printf "%(%w)T" "${1}/1/${2}")
(( dow == 0 )) &&...