Cell-free massive MIMO (multiple-input multiple-output) is a promising network architecture for beyond 5G systems, which can particularly offer more uniform data rates across the coverage area. Recent works have shown how reconfigurable intelligent surfaces (RISs) can be used as relays in cell-free massive MIMO networks to improve data rates further. In this paper, we analyze an alternative architecture where an RIS is integrated into the antenna array at each access point and acts as an intelligent transmitting surface to expand the aperture area. This approach alleviates the multiplicative fading effect that normally makes RIS-aided systems inefficient and offers a cost-effective alternative to building large antenna arrays. We use a small number of antennas and a larger number of controllable RIS elements to match the performance of an antenna array whose size matches that of the RIS. In this paper, we explore this innovative transceiver architecture in the uplink of a cell-free massive MIMO system for the first time, demonstrating its potential benefits through analytic and numerical contributions. The simulation results validate the effectiveness of our proposed phase-shift configuration and highlight scenarios where the proposed architecture significantly enhances data rates.