An apparatus includes a shaft, an expandable dilation member, and a bulbous tip. The shaft has a first outer cross-sectional dimension. The dilation member is positioned proximal to the distal end of the shaft. The dilation member is operable to transition between a non-expanded configuration and an expanded configuration. The dilation member is sized to pass through a passageway associated with drainage of a paranasal sinus or a Eustachian tube when the dilation member is in the non-expanded configuration. The bulbous tip is positioned at the distal end of the shaft. The bulbous tip is distal to the dilation member. The bulbous tip has a second outer cross-sectional dimension. The second outer cross-sectional dimension is larger than the first outer cross-sectional dimension. The bulbous tip is removably secured to the distal end of the shaft.