100% possible, might require some knowledge of the html replacements Vince linked to. What sort of information is needed to be entered manually? Attack bonus, damage bonus etc? Do you have no attributes stored in Roll20 at all?
The essence of a drop down query is to give set results based on your selection, if all you need to do is vary the attack/damage mod then you are best off with a basic template like your example with manual queries:
&{template:default} {{name=Attack}} {{attack=[[1d20 + ?{Attack Modifier}]]}} {{Damage=[[?{Damage Calculation}]]}}
You could replace the attack/damage calculation with a couple of preset options though:
&{template:default} {{name=Attack}} {{attack=[[1d20 + ?{Attack Modifier|Melee,2|Ranged,3}]]}} {{Damage=[[?{Weapon|Sword,1d8+2|Dagger(Melee),1d4+2|Dagger(Thrown)|1d4+3}]]}}
To only have 1 query to rule them all you will be in html replacement territory but once we know more of your setup we can address that accordingly with some examples for you :)