Almost exactly the way you described it:

print "$_: ", /^\w+$/ && !/^\d+$/ ? 'Good' : 'Bad' for qw[ abc a1c 1b3
+ 123 ];;
abc:  Good
a1c:  Good
1b3:  Good
123:  Bad
[download]

Or if you insist on a single regex:

print "$_: ", /^(?=.*[a-zA-z])\w+$/ ? 'Good' : 'Bad' for qw[ abc a1c 1
+b3 123 ];;
abc:  Good
a1c:  Good
1b3:  Good
123:  Bad
[download]

Though it is doubtful if it is any more efficient; and is certainly less clear.