Undereamed piling has normally been either 1) using reaming tool lowered down pile shaft, followed by manual clean of base. 2) hand mined with timber support to roof of chamber.
In the UK, modern practice (post Construction Design & Management Regulations) is to regard man access in pile shafts as an avoidable risk.
Under-reaming with tools requires ground to stand unsupported for a reasonable time period i.e. not suitable for sandy cohesionless soils.
In any case, underreaming is normally employed to increase base capacity of piles in clay soils. If there is sufficient thickness of a sandy soil it should be possible to achieve relatively high base capacity without underreaming.