Nothing wrong with using a primer pump for this type of issue if you have already changed everything for new... and dont want to invest any more time tracking down the cause.
2 days does seem like there could be more than just evaporation going on, especially at only 45°... but a pusher pump will be a fix or band aid to get around whatever the problem is.
Have you seen these pumps? Cheaper priced than the bigger carter electric pumps and quite a bit smaller. Read online of someone else using this for a primer pump, this one is cheaper than MSRP.
https://www.ebay.com/itm/28630334268...4&gad_source=1