לא תאחוז בה חברתה בידיה בשעת טבילה אלא אם כן רפתה ידה כדי שיבואו המים במקום אחיזת ידיה ואם הדיחה ידיה במים תחלה שרי שמשקה טופח שעל ידיה חבור למי המקוה :
Another woman should not hold her in hand while she is immersing, unless she loosens her hand so that water will come into the place where she is holding. And if she rinses her hand in the water beforehand, it is acceptable, because the liquid drops on her hand connect to the mikva water.
A very similar problem comes up all the time with tevilas kalim, immersing veseles that one bought from a non-Jew. Holding the glass (for instance) tightly is a chatzitza, and letting go of it will cause it to break. What to do? There are two options. 1) hold the glass loosely so that water could get between your hand and the glass. 2) get your hand wet before grabbing the glass.
Either one of these could be applied here. Get the wheelchair wet before the woman sits down, or for her to raise herself up just a little so water can get in between herself and the chair in the mikva.