No, you can't use a Athletics check instead.
The Constrict attack must be used as is, since it is not a Strength (Athletics) roll, it's an attack. If you're interested in improving other Wild Shaped forms' ability to grapple, this information might come in handy.
The rules for the druid's Wild Shape feature say that:
Your game statistics are replaced by the statistics of the beast, but you retain your alignment, personality, and Intelligence, Wisdom, and Charisma scores. You also retain all of your skill and saving throw proficiencies, in addition to gaining those of the creature. If the creature has the same proficiency as you and the bonus in its stat block is higher than yours, use the creature’s bonus instead of yours.
So when making the Athletics check required by the grapple, you would use the Wild Shape form's Strength (Athletics) statistics, but if the creature did not have proficiency in Athletics (or has a lower proficiency), then yours would apply.