In the nutshell - Yes you can disconnect the amp meter and install a voltmeter.
Volt Meters or Voltmeters are easy for folks to understand with scales of volts at the battery being displayed, while amp meters or ammeters confuse folks with the simple + and - scale. There are also a few different designs of them to add to the confusion.
So if you want to go with an easy to read Volt Meter, and If you have factory original 68 saw tooth gauge pac on the console you can buy a voltmeter from AAW- American Automotive Wire at http://factoryfit.com
that is a dead ringer for the original "Battery" amp meter. Think it was around 150 bucks last time I checked. Just remove the current gauge from the pack, alter the wiring as per directions included with the gauge and you are good to go and most folks would not notice your battery gauge has battery readings in volts vs -40 to +40 of the factory unit.
If you are currently using an aftermarket gauge pack check with the gauge vendor to see if they make a volt meter in that design style.
As to the mystery of a true amp meter, yes the original purpose and design is that they were part of the charging circuit reporting on its current state charging or exhausting reserves and most did deliver full power to the gauge - therefore into the passenger compartment and could short or cause fires. These style gauges were common in MOPAR and some Ford vehicles. As the wiring aged and insulation cracked they shorted out and could lead to fires. MAD Electric has a good tech doc on removing a MOPAR style system on their website.
GM's approach was NOT to direct full power leads to the gauge. The GM "Amp meter" is actually more like a multimeter diagnostic tool registering the condition of the system between two points - the horn relay bus-bar and the junction block behind the battery. If it finds more power on one side then the other you get positive or deflective results on the gauge face.
So it is as safe as it can be. To figure out where your issue is test the wiring to the gauge to see if it is intact and in working order. Test by disconnecting the gauge then seeing if you have a circuit with a test light or probe to ground on each leg of the gauge connection plug will test the wiring. If you get nothing on one or both you have a wiring issue, if you get good results on both the gauge unit itself is dead. The dead original factory amp meter can be replaced with a quality reproduction unit from Classic Headquarters with no modifications.
If your testing results point to a wiring issue please note that as a safety measure the factory wiring had a "fusible" link at each end of the connection points, most likely orange in color. Check these for signs of fusing from overloads - brittle, crunchy, physically discolored. The black wire with orange link should be connected behind the battery in the "junction block". The black with white stripe wire and orange link should be connected to the horn relay "Bus-Bar". If you find the link(s) have fused you can replace the link with same gauge from any auto parts store. If they seem okay just check to see if they are terminated and connections on the bus and block are clean and tight. Both wires run back to the bulkhead connector in positions S-A & S-B you can also check on the drivers side once you remove the fuse panel cover in same locations S-A & S-B. If those points are tight check continuity from the connector at the console to fuse panel, fuse panel to bulkhead connector side, bulkhead connector to horn relay bus and bulkhead to junction block. Somewhere you will find the gap in the circuit.