actually, I just googled blood-injection-injury phobia - goodness, that is a lot to have on your plate.
As someone who has had a planned cs, I'd say there is a fair bit of needle work involved (an iv line for the op, needle for spinal/epidural, although you don't need to see that - post op fragmin injections for 5 days afterwards).
In terms of blood, I saw very little. Mostly what ds was covered in when they held him up!
In terms of injury - there is an abdominal incision, but there are dressings and they tend to be small and neat, and are surgical (not sure if this makes any difference to you at all).
In theory it is possible to have a vb with little intervention, and you might be lucky enough, with your first, to have no problems and no tearing. tbh this would put you in a minority (most women tear with their first) but it can happen.
Generally speaking, planned cs offers you a known set of risks and interventions, that you can try and manage and mitigate beforehand, versus a much less known outcome with a vb. In terms of your phobias, it depends a lot on how bad they are and how you have managed them in the past, I think. For example, an intervention free vb would involve a lot less needle work than a cs - but a vb with a lot of intervention and problems would give you a lot more to deal with than a planned cs.