When you say standard batteries, are you talking about alkaline cells? They are nominally rated at 1.5 v each.
Nickel-Cadmiun & Nickel Metal hydride are 1.2 v each.
They are normally placed in series, so you just add the number of cells to get your voltage output.
e.g. 3 cells of alkaline will give 4.5 v and 3 re-chargeable will only give 3.6 v, though initially, after a full charge, the
3-cell pack will give over 4 v so your inserting standard cells should not be a problem.
Providing the corrosion hasn't developed into what they call 'black wire' corrosion, there should not be a problem.
If you can check the resistance of the negative wire from the cell connector to the PC board, it should read virtually nil. If the connector is soldered directly to the board, ignore the above.
The mA rating of the battery pack will give a certain amount of operating time. If you can get a higher capacity into the same physical space, go ahead. If you get a lower rating than you had in the first place, you'll be recharging more often. No point in that. As the others quite rightly pointed out, all the corrosion deposits should be removed. Good luck.