As others have said, no this can't be done. And certainly not via the symbol table because lexicals don't live there.

PadWalker provides a function called peek_sub which will tell you the names of lexical variables used within a sub. However, not all lexical variables necessarily correspond to parameters. The sub might contain, say, a foreach my $x (@array) loop where $x is just a loop variable; nothing to do with a function parameters.

A better alternative would be to write your module using one of the many CPAN extensions that provide declarative sugar for method signatures, and provide an introspection API. Here's an example using Kavorka:

use v5.14;

package Module1 {
    use Moo;
    use Kavorka;
    
    method allVars (Int $no1, Int $no2, Str $name1, Str $name2) {
        say "all vars = $no1 $no2 $name1 $name2";
    }
}

say "Let's check the method call works...";

my $obj = Module1->new;
$obj->allVars(1, 2, "Foo", "Bar");

say "Now let's inspect its parameters...";

my $info = Kavorka->info(\&Module1::allVars);
for my $parameter ($info->signature->positional_params)
{
    say $parameter->name, " has type ", $parameter->type->name;
}
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The output is:

Let's check the method call works...
all vars = 1 2 Foo Bar
Now let's inspect its parameters...
$no1 has type Int
$no2 has type Int
$name1 has type Str
$name2 has type Str
[download]

Function::Parameters would similarly work. Method::Signatures would not because although it provides very similar declarative sugar, it doesn't seem to have an introspection API. MooseX::Method::Signatures would also work, but it's incredibly slow.