Why do you want to avoid the additional block? Since the finally block contains "normal" operations which may throw an exception AND you want the finally block to run completely you HAVE to catch exceptions.
If you don't expect the finally block to throw an exception and you don't know how to handle the exception anyway (you would just dump stack trace) let the exception bubble up the call stack (remove the try-catch from the finally block).
If you want to reduce typing you could implement a "global" outer try-catch block, which will catch all exceptions thrown in finally blocks:
try {
try {
...
} catch (Exception ex) {
...
} finally {
...
}
try {
...
} catch (Exception ex) {
...
} finally {
...
}
try {
...
} catch (Exception ex) {
...
} finally {
...
}
} catch (Exception ex) {
...
}