While I deeply value other people self-applying 'transsexual' for whichever reason matters to them, I prefer 'transgender' as an adjective for me if I'm forced to choose anything. I expect that's due to the personal definitions of sex and gender I use since I can't make myself see them as divorced subjects. I can certainly understand the usefulness of seeing sex as purely biological and gender as sociocultural aspects for others but, in my mind, it feels like an artificial separation of two things stuck in a muddied circular relationship.
When it comes to physical characteristics, I have a habit of seeing the construction of definitions as somewhat gendered in nature because I believe it's important to emphasise that the scientific process doesn't take place in a bubble separated from all human complications. Flowing from that, the crafting of sex classifications often seems to start from a point greatly impacted by ingrained assumptions about the gender binary and leads to those assumptions being imposed on nature. I'd suggest that might be highlighted by factors like the way definitions of sex have varied greatly throughout history and continue to vary depending on contextual need (e.g. expected gamete production, expected chromosomes, visible secondary sex features, hormone levels, etc), or cases wherein newborns are assigned to a sex based on which side of the binary their genitalia are subjectively deemed closer to matching.
Ultimately, this and much more means I'll see myself as changing my overall gender even when changing things like secondary or primary sex characteristics and believe it's my gender that tends to determine which definition of sex people apply to me. In every day contexts, if a person sees me as a woman then I think they'll apply a definition of sex that classifies me as female, thus my sex would be gendered in nature. Of course, if other people prefer to look at the causal relationship as reversed thereby inclining them towards self-applying 'transsexual' then I can totally understand that too. The same understanding applies to people that state there's a strict separation between sex and gender too.
Anyhoo, I'm very tired and anxious due to an important gate-keeping appointment soon so this might not make any sense at all and is probably a total ramble. Well, what I mean is that I expect things I write generally don't make sense but that's probably even more applicable here. *giggles*