You know, I made a comment earlier about the UK context. Let me expand on that a little, as this thread has been sent down a major diversion by one person mis-interpreting scientific studies.
Michel Odent argues that the conditions should be right for normal straightforward vaginal delivieries in most women and then that if complications occur clinicians should move swiftly to a caesarian. The thing is, at the moment the way women labour and give birth in hospitals in the UK often does not give them the optimal conditions for achieving straightforward vaginal delivieries. I believe this is the model that operated at Pithiviers.
If someone genuinely wants to avoid an instrumental birth, which I personally do not think is unreasonable given the associated risks, then probably the best things they can do is find ways to make a straightforward spontaneous vaginal birth as likely as possible. This might mean, for example, preparing for non-medical ways to deal with the intensity of labour (e.g. using hypnosis), ensuring they have good support from a birth partner, and if possible continuity of care from a midwife they know (in the UK this usually means opting for homebirth or an independent midwife), avoiding as much stress as possible during labour and labouring in a comfortable homely environment, not birthing lying on your back, avoiding induction or acceleration of labour, avoiding an epidural etc etc etc. These things will not always be possible in all circumstances for all women.
Additionally, having a discussion in advance of labour about fear of instrumental delivery and flagging up and documenting your strong preference to avoid it or indeed advance warning that you will not consent to it, may alter the way you are cared for if things do not go to plan. Knowing you would refuse a late attempt at an instrumental delivery might, for example, mean caregivers would consider a c-section sooner to try to avoid a time-critical situation where the baby is stuck. This already happens in a way in homebirths, where midwives are considering transfer to hospital in time for other measures to be taken if there are problems.
Once you are in the situation of having been pushing for 2 hrs and baby is not coming out and beginning to look comprimised because of heartrate dipping or whatever, then as viva says, the instrumental delivery may at that point offer significantly less risk to the baby. You can of course still decline it if you choose, just as you could indeed decline a c-section as well, even if it would be detrimental to the health of both you and the baby.