Is it possible that universe might not be speeding up expansion? I'm not sure but I was thinking of galaxies shrinking with time while still moving apart from each other at almost a constant speed or less (i.e: uniform/slightly decelerating expansion). This may need further evidence such as tracking the distance between stars inside our galaxy to check if they are getting closer.
If so, would this make an alternative explanation for visualizing the universe as if it were expanding in an accelerating rate?
 A: I don't see any logical connection to accelerating expansion. If shrinking of galaxies could explain away the acceleration of the expansion, then it could  also explain away the expansion itself.
Regardless of whether we're talking about expansion or acceleration of expansion, the effect isn't measured by watching the apparent sizes of galaxies get smaller over time. It's determined mainly by measuring Doppler shifts.
It's true in a very abstract sense that if all objects in the universe were shrinking, while the distances between galaxies stayed the same, the observable effect would be exactly the same as expansion of the universe. But this would require all objects to shrink uniformly, including people, solar systems, measuring sticks, and hydrogen atoms. In general relativity, this is known as general covariance.
A: First of all, galaxies don't shrink. If our own galaxy were shrinking, then we would be moving towards our galactic centre, and we would observe a blueshift in that direction.
Second, the accelerated expansion can be determined from the relation between redshift and brightness of distant supernovae. Neither redshift nor brightness would be affected by shrinking galaxies.
And third, the expansion of the universe started to accelerate when the universe was 7.7 billion years old. Before that time, the expansion was decelerating. This can be explained in a straightforward way by the Standard Model - the expansion accelerated when dark energy became dominant - and I don't see how it could be easily explained by any other mechanism.
