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GH-38447: [CI][Release] Don't use "|| {exit,continue}" (#38486)

### Rationale for this change

If we use "|| {exit,continue}", "set -x" doesn't work.

With "|| exit" ("false" in "a()" doesn't stop the shell execution):

```console
$ cat /tmp/with-or-exit.sh
set -e

a()
{
    false
    echo "a: failed after"
}
a || exit 1
echo "top level"
false
echo "failed after"
$ bash /tmp/with-or-exit.sh
a: failed after
top level
```

Without "|| exit" ("false" in "a()" stops the shell execution):

```console
$ cat /tmp/without-or-exit.sh
set -e

a()
{
    false
    echo "a: failed after"
}
a
echo "top level"
false
echo "failed after"
$ bash /tmp/without-or-exit.sh
```
### What changes are included in this PR?

* Remove needless `|| exit`
* Use `if` instead of `|| continue`

### Are these changes tested?

No.
* Closes: #38447

Authored-by: Sutou Kouhei <kou@clear-code.com>
Signed-off-by: Sutou Kouhei <kou@clear-code.com>