You've a month to prepare yourself emotionally. You clearly know that your reaction ("ugly tears" that are "not necessarily happy") WILL happen, as at this point you've created a self-fulfilling prophecy even if you weren't already inclined towards this emotional display already.
I'm not without sympathy and empathy for you - my father had a horrific accident when I was 18 years old (made even worse due to the fact that it happened at home) that resulted in catastrophic brain damage for him. He was in hospital in a "basically no brainwaves" coma for 6 months, and while he survived the multiple initial surgeries and "awakened" from the coma (so to speak) eventually, he was in a basically "just above vegetative" state and was bedridden, completely incontinent/had to wear diapers, and needed a feeding tube in his stomach as the muscle atrophy that occurred during his coma meant that he could no longer swallow/take food/liquid orally. My family's culture (I'm adopted, but adoptive family is Hispanic/Mexican) meant that we take care of our elderly/disabled family members, no matter what. No putting them in facilities/care homes. You handle it yourselves as a family.
So that was it for me, future decided for me at age 18. I never moved out, never finished uni, never got married, never had kids, never had a career (I was a full-time primary caregiver for my dad and worked at the family business as well.) My dad lived another 21 years in this awful state (I hoped every day that his brain damage was severe enough that he did not "realize" the situation/condition he was in, as awful as that sounds.) He died in 2021 when I was 39 years old. My older sister, who did the same as me (stayed living at home, worked for family business/as a caregiver, basically had even less of a social life than I did) was 45 when he died.
So while I genuinely feel for you, as I understand exactly what you went through with your mother's cancer through your childhood and young adulthood - you and your sister still have time. She's not moving to another country. She's not sick/dying/dead herself. She's only getting married. Unless your plans to "share that carefree experience as single, unmarried people" meant that you would be sleeping with random blokes while barhopping/clubbing, I fail to honestly see why you and your sis can't have that "carefree experience" as a married person (her) and someone who is in a "happy relationship" (you.) Again, unless you two were planning to party hard and hookup with dudes casually, very little has changed in terms of having a "carefree experience" with your sister. I'm sure your sister's future husband and your partner would be very understanding of you two having girls' trips (without the hookups) etc. as I imagine they both know what you and your sister went through. The only things that have changed is that you're not literally in your early 20s and you can't casually have hookups with guys you meet on any vacations/trips.
Again, you've a month to emotionally prepare yourself and PREVENT your self-fulfilling prophecy of "I'm going to ugly cry unhappy/sad tears at my sister's wedding." Whether that requires more counselling (or counselling of a different sort perhaps?), or a plan for what you will do when you feel the ugly crying approaching (tastefully remove yourself from the ceremony/reception until you have yourself under control), you have weeks to get yourself ready and NOT potentially make a portion of your sister's wedding about yourself. Because that is what you are currently doing.
Have you stopped to even ask yourself how your SISTER feels about all of this? Maybe SHE wants to ugly cry at her OWN wedding, as she had the same childhood/early 20s time period devoted to taking care of your mother.
Perhaps you should have a talk with her about this whole thing, have a good cry together over the death of lost time/lost young adulthood, and move on together.