missed the point?
My thinking is this: on a big hunt I can have the rifle set up for the target animal, but if along the way I want to do some varminting I can switch over. The question: What to do about the scope, short of memorizing the ballistics table for the weights and powder charges and distances.
I think the OP is not asking about switching scopes, but about what to do when switching ammo (big game - varmint).
He mentions a .243, and also mentions both target animal (big game) and varmints. SO, what is the difference, in his rifle, between the big game ammo (100/105gr bullets) and his varmint ammo (70?80?90?gr bullets)?
There are only two practical ways to do it, and only one that is common. Either use a separate scope for each, zeroed for the ammo to be used, or use a single scope, and learn the differece in the adjustments needed for proper zero (the most common way).
With the T/C Contender ( & Encore), since the scope mounts on the barrel, once zeroed, they (usually) return to zero pretty well. However, any time you dismount and remount a scope there is a chance it will not be at proper zero, so one should ALWAYS check by firing test groups.
Leaving one scope mounted retains the zero you set (unless something happens to knock it out of alignment, like the case falling out of the airplace onto the pavement during baggage handline, etc). It is always a good idea to verify the zero before starting the hunt.
What most of us do is zero for our main load (deer load?), and then shoot the varmint load, and see where it hits on the target. Memorize (write down) how many clicks, in which direction(s) you need to move the crosshairs to zero for the new load. Then just adjust the scope for one load or the other by counting the clicks.
Some people tape a card with the info on the stock, some keep it with their hunting license, or some other place it won't get lost. Some people use this method for adjusting for the range also. Zero at 100yds, then when the game is 250yds, look at the card and add in the right number of clicks to hold dead on.
others of us just use Kentucky Windage, keeping the same sight setting, but holding "off" the estimated amount. For example, if I know that my deer load hits 2 inches higher and half an inch to the left at 100yds than my varmint load (for example) I can either crank in the adjustment to the scope, or just put the crosshairs a bit "off" to get the hit. Both ways work, but holding off requires your estimates to be correct, in both range/windage AND hold off aim. Faster, but not as precise.
Better (easier) for big game, where you may have time, and other pressure on the shot, where an inch or two difference still gets you a good hit. For small targets like varmints, a slight misestimation of hold can mean a clean miss, so its usually better to dial in the scope for the small targets, and adjust back for big ones, if you have time, or hold off, if you don't.