Neither company cares
My experience is that both companies are strong and secure enough to not worry about you leaving once hired and thus they don't really care if you have those tickets. I had the FE written when I interviewed at SWA, and although it wasn't on my resume (no need) I'm sure that they knew about it when they did the records check. It never came up during the interview, but I was prepared to discuss why I had it if it did. I got my type and entered "the pool".
I was in the pool at SWA with my 737 type when FedEx called and I went to interview there. Again, the 737 type wasn't on my online app with them, and the subject never came up during the interview. I was prepared to discuss my position in the SWA pool if it came up in the interview also, but it never did.
After I started at FedEx and moved to Memphis I had to update my status and address with SWA, and I told them that I was working at FedEx. That was never an issue with them, in fact they offered to hold off contacting FedEx until I was offered a class date. After the first year in the pool they gave me a positive space pass to Dallas to update my records and get finger printed in order to remain in the pool, again knowing full well that I was working for FedEx. That is why I say they are a class act and not worried about pilots leaving for greener pastures. At that point I was still honestly debating with my family the merits of jumping over to SWA once I got a class date.
After more than 2 years in the pool at SWA I was offered a class date but by that time I had too much time invested at FedEx to leave. SWA offered me the chance to defer my decision and class date for 6 months to ponder the situation, still knowing full well that I worked for FedEx. I chose not to defer.
SWA is a first class company, and they know that if you want to work there you will most likely stay there regardless of who else comes calling (in today's environment, I know this wasn't necessarily the case years ago). If I could have gotten on at SWA first I would never have left, but I just couldn't wait around for over 2 years to continue my aviation career.
You never know when your backup plan in this business will become your primary plan. You owe it to yourself and your family to make yourself as competitive as you can to as many quality companies as you can. Class companies like SWA and FedEx understand that and won't hold it against you because you are trying to stack the odds in your favor. Get as many tickets as you can that will increase your chances of getting that interview.
Good luck.
FJ