Hi Iuri,
the proper process to achieve this is using Javascript. The logic is that you have a second container (the second drop down), which is not filled with any values (it is empty). Maybe you don't even show it (you can hide it).
But to solve your problem, why don't you say and put this at the top of your page?
for {set i 0} {$i < [ns_set size $myform]} {incr i} {
set varname [ns_set key $myform $i]
set $varname [ns_set value $myform $i]
}
}
set child_id [set cat_${category_id}]