I guess the only thing that worries me about doing med is that there is compulsory surgery involved and as I suck at physical tasks (or at least I think I do - never been good at sports, handwriting, can be quite clumsy). I just don't want to harm anyone during the compulsory surgery because of my physical shortcomings.
You sound just like me! And I coped with "surgery" as a med student just fine - a lot of the time you're only observing and not "scrubbed in" (not in a sterile gown & gloves etc and therefore not allowed in the sterile field) anyways; and when you do get to scrub in and assist, it generally involves holding retractors, and you might get to hold the scope on laparoscopic surgery (but don't worry, if you turn out to be bad at it they'll swap you off the scope). You may get to do some suturing in relatively low-stakes settings (removing skin lesions from someone's back, suturing a cut on someone's arm/leg)
after you've had a practical class on suturing. It's good to keep in mind that the doctors and surgeons supervising you also don't want any harm to come to anyone due to "med student ineptitude" so as a student you'll rarely (if ever) get to do anything that carries significant risk of harm; those will be activities you can only observe.
And as govpop mentioned, you'll get taught how to do bloods (venepuncture - obtaining specimens for blood tests) and IV lines (IV cannulation), and those are more "bread and butter" junior doctor tasks. They are more learned tasks that you'll get better at with practice.
PS: during our clinical years (years 4-6 at Otago, of which I only attended 4-5), only some sessions in the operating theatre were required (being caught up in the surgical fever, though, I went to a few more than I needed), and even when your attendance is required, "scrubbing in" (thorough handwashing followed by meticulous donning of sterile surgical gown and sterile gloves) is generally voluntary (for us it was offered at the surgeon's discretion and it was a perk that we eagerly took up for a better view of the action). I'd imagine there would be some faint-hearted med students who would prefer not to scrub in, and I've not heard of anyone getting in trouble for declining to scrub in as a student.
PPS: After graduation, House Officers (interns/residents for Aussies) attached to surgical teams generally stay on the wards and look after the ward patients, with minimal (if any) theatre time; and after that, you'd have to become a surgical or anaesthetics registrar to find yourself in theatre.