וַיַּעֲבֹר מָרְדֳּכָי וַיַּעַשׂ כְּכֹל אֲשֶׁר־צִוְּתָה עָלָיו אֶסְתֵּר׃
So Mordecai passed and did just as Esther had commanded him. (Ester 4.17)
Targum says (first):
וּנְסֵס וּכְנֵס מָרְדְכַי וַעֲבַר עַל חֶדְוַת חַגָא דְפִסְחָא וְצוֹמָא גְזַר וִיתֵב עַל קִטְמָא וַעֲבַד כְּכָל דִי פַקְדַת עֲלוֹי אֶסְתֵּר:
Rashi ad loc:
וַיַּעֲבֹר מָרְדְּכָי. עַל דָּת, לְהִתְעַנּוֹת בְּיוֹם טוֹב רִאשׁוֹן שֶׁל פֶּסַח,
Mordechai passed. [he transgressed] the law by fasting on the first festive day of Pesach
My logic says exactly the opposite - the celebration of Pesach is the greatest testimony of G-d saving His people from the final solution, saving their bodies (unlike Chanukka) and intervening against their worst enemies. In the Aggadah, we say that in every generation our enemies raise against us and G-d saves us from them.
(This seems to fit Kaballically - Giluy Yesod Aba etc.)
Therefore, keeping Pesach and showing our Bitachon in Hashem seems to be a natural choice, especially acknowledging the fact that the decree was to be executed in 11 months!
A bonus point would be saying "זכר ליציאת מצריים" on Purim also!
Why didn't Mordechai and Ester consider this option?