Integration of hyperspectral imaging into fluorescence-guided neurosurgery has the potential to improve surgical decision making by providing quantitative fluorescence measurements in real-time. Quantitative fluorescence requires paired spectral data in fluorescence (blue light) and reflectance (white light) mode. Blue and white image acquisition needs to be performed sequentially in a potentially dynamic surgical environment. A key component to the fluorescence quantification process is therefore the ability to find dense cross-modal image correspondences between two hyperspectral images taken under these drastically different lighting conditions. We address this challenge with the introduction of X-RAFT, a Recurrent All-Pairs Field Transforms (RAFT) optical flow model modified for cross-modal inputs. We propose using distinct image encoders for each modality pair, and fine-tune these in a self-supervised manner using flow-cycle-consistency on our neurosurgical hyperspectral data. We show an error reduction of 36.6% across our evaluation metrics when comparing to a naive baseline and 27.83% reduction compared to an existing cross-modal optical flow method (CrossRAFT). Our code and models are publicly available ( https://github.com/charliebudd/x-raft-cross-modal-non-rigid-registration ).