In this paper, we thoroughly elaborate on the impact different transmit-antenna selection (TAS) strategies induce in terms of the outage performance of incremental cognitive multiple-input multiple-output (MIMO) relaying systems employing receive maximum-ratio combining (MRC). Our setup consists of three multi-antenna secondary nodes: a transmitter, a receiver and a decode-and-forward (DF) relay node acting in a half-duplex incremental relaying mode whereas the primary transmitter and receiver are equipped with a single antenna. Only a statistical channel-state information (CSI) is acquired by the secondary system transmitting nodes to adapt their transmit power. In this context, our contribution is fourfold. First, we focus on two TAS strategies that are driven by maximizing either the received signal-to-noise ratio (SNR) or signal-to-interferenceplus-noise ratio (SINR), and extend their operating mode into an incremental relaying setup where MRC is carried jointly over both relaying hops. Second, given the inherited complexity, we proceed by the exact outage analysis of the direct (first-hop) transmission as a preliminary yet innovative step pertaining to the SINR-driven TAS strategy. Third, the end-to-end (secondhop) transmission outage performance is also evaluated although shown to entail an involved derivation roadmap for both TAS strategies. Forth, we simplify our exact derivations by means of the asymptotic analysis which reveals that the detrimental effect of mutual interference on the secondary system is originated from the primary transmitter (i.e., co-channel interference) and not from the primary receiver (i.e., interference threshold). That is, even if the secondary system operates at a high tolerated amount of interference, an outage floor will still occur because the primary system will pump a high amount of co-channel interference in return. The SINR-driven TAS shows up as an optimal interference-aware strategy in this regard. It achieves the same diversity gain but a better coding gain compared to its SNR-driven counterpart. The correctness of our results is confirmed by Monte Carlo simulations and the actual outage gap between both TAS strategies is reflected.