Is there a dramatic effect of playing a player with 99%. I know it seems silly and tedious, but there is an off day in two hbd days. 

not serious at 99 however when you get lower then that their is a drop off and more chance of injury.. some additional food for thought that one off day will probably not be enough to rest a position player to a point where you will be able to run him out 9 innings every day for the rest of the season.. As a general rule most players will need around 20 games of a season or so to remain at 100%... I like to give guys time off in bunches and not everyone as the same time.

In my experience the fall off occurs defensively and not at the plate. 99, you probably won't see any difference, but as it gets lower and lower you'll notice the difference.
I usually target 95 as an absolute  floor, but have in the past gone as low as 92. 

As fasteddy mentions the chance for injury climbs the lower the % gets. Which is probably the biggest risk of playing a guy who is fatigued.

That said, 99% wouldn't phase me at all. Especially if I were in a playoff race or jockeying for a first round bye.

Over the years, I've found that injury risk is much higher at 97%.    This is based on minor league players because I seldom drop BL below 98%.   But the vast majority of my minor league injuries come at 97% or below.   I only check minor league fatigue on the weekend so there's a decent sample size to work with.