sorry, I think we are at an empass.
if you want 10,000 columns divided, I dont see another option than writing code that divides them all.
Unless you are hinting that you expect certain columns to be duplicates, in which case you might optimise to skip these, or borrow the values from similar columns, but in the general case. No, theres no way to do all the calculations you said you wish to do without .. doing them...
However it is the case the tidyverse/dplyr trades away performance for its friendly syntax.
So you could use a faster way to do all the divisions by using data.table package. This has its own syntax that you can learn. also, lately there have been improvements to the dtplyr package (extra t between the d and the p) this lets you make your instructions in dplyr syntax but then uses data.table to do the calculations.
I think you would see a speed up with the data.table back end. However, it would still be performing numerous divisions (as it seems thats what you require)