I know this is a super old thread, but I wanted to put the solution in that I have been using. I borrowed it from https://github.com/RamblingCookieMonster/PSSQLite/blob/master/PSSQLite/Invoke-SqliteQuery.ps1
this project scrubbed it out using a bit of imbedded c# code that is very efficient and clean:

if ($As -eq 'PSObject') {
    #This code scrubs DBNulls.  Props to Dave Wyatt
    $cSharp = @'
using System;
using System.Data;
using System.Management.Automation;

public class DBNullScrubber
{
    public static PSObject DataRowToPSObject(DataRow row)
    {
        PSObject psObject = new PSObject();
        if (row != null && (row.RowState & DataRowState.Detached) != DataRowState.Detached)
        {
            foreach (DataColumn column in row.Table.Columns)
            {
                Object value = null;
                if (!row.IsNull(column))
                {
                    value = row[column];
                }
                psObject.Properties.Add(new PSNoteProperty(column.ColumnName, value));
            }
        }

        return psObject;
    }
}
'@

    try {
        if ($PSEdition -eq 'Core') {
            # Core doesn't auto-load these assemblies unlike desktop?
            # Not csharp coder, unsure why
            # by fffnite
            $Ref = @( 
                'System.Data.Common'
                'System.Management.Automation'
                'System.ComponentModel.TypeConverter'
            )
        } else {
            $Ref = @(
                'System.Data'
                'System.Xml'
            )
        }
        Add-Type -TypeDefinition $cSharp -ReferencedAssemblies $Ref -ErrorAction stop
    } catch {
        if (-not $_.ToString() -like "*The type name 'DBNullScrubber' already exists*") {
            Write-Warning "Could not load DBNullScrubber.  Defaulting to DataRow output: $_"
            $As = 'Datarow'
        }
    }
}


# to use it to convert the DBNull into $null I use it like this:

try {
    $CSBuilder = New-Object System.Data.Odbc.OdbcConnectionStringBuilder
    $Cred = Get-Credential -Message "Please provide credentials for $Server"
    $OdbcDriverName = 'SQL Server'
    $CSBuilder['driver'] = $OdbcDriverName
    $CSBuilder['DSURL'] = $Server
    #$CSBuilder['Database'] = 'master'
    $CSBuilder['Database'] = $Database
    $CSBuilder['uid'] = $cred.UserName
    $CSBuilder['pwd'] = $cred.GetNetworkCredential().Password
    $CSBuilder['EncryptedPassword'] = 2
    $CSBuilder['ConnectionIdleTimeout'] = 600

    $conn = New-Object System.Data.Odbc.OdbcConnection
    $conn.ConnectionString = $CSBuilder.ConnectionString
    $conn.ConnectionTimeout = 30
    $conn.Open()            
    #$conn.ChangeDatabase($Database)

    $cmd = New-Object System.Data.Odbc.OdbcCommand($QryText, $conn)
    $cmd.CommandTimeout = 30

    $ds = New-Object System.Data.DataSet
    $da = New-Object System.Data.Odbc.OdbcDataAdapter($cmd)
    [void]$da.Fill($ds)

    switch ($As) {
        'DataSet' { return $ds }
        'Table' { return $($ds.Tables[0]) }
        'Row' { return $($ds.Tables[0].Rows[0]) }
        'PSObject' {
            foreach ($row in $ds.Tables[0].Rows) {
                #--- DBNull scrubber conversion ---#
                [DBNullScrubber]::DataRowToPSObject($row)
            }
        }
        'SingleValue' {
            return $ds.Tables[0] | Select-Object -ExpandProperty $ds.Tables[0].Columns[0].ColumnName
        }
        default { return $ds }
    }
} catch {
    Write-Warning "Query failed: $($_.Exception.Message)"
}