Is it possible to get schema ID in another database without using dynamic sql?
To answer the question literally, no there isn't a way to do this in T-SQL without using dynamic SQL (but see Aaron's suggestion to use a view).  You can, however, use a SQLCLR function (which can be called from a T-SQL function).  The following is demo code to illustrate the principle:

-- Returns 7 from any database context
SELECT dbo.GetSchemaID (N'AdventureWorks2012', N'Production');


T-SQL script:

CREATE ASSEMBLY [CLR] AUTHORIZATION [dbo]
FROM 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WITH PERMISSION_SET = SAFE;
GO
CREATE FUNCTION [dbo].[GetSchemaID] (@DatabaseName [nvarchar](4000), @SchemaName [nvarchar](4000))
RETURNS [int]
AS EXTERNAL NAME [CLR].[UserDefinedFunctions].[GetSchemaID];


C# source:


using System;
using System.Data;
using System.Data.SqlClient;
using Microsoft.SqlServer.Server;

public partial class UserDefinedFunctions
{
    [SqlFunction
        (
        DataAccess=DataAccessKind.None,
        IsDeterministic=false, 
        IsPrecise=true, 
        SystemDataAccess=SystemDataAccessKind.Read
        )
    ]
    public static int GetSchemaID(string DatabaseName, string SchemaName)
    {
        using (SqlConnection conn = new SqlConnection("context connection = true"))
        {
            conn.Open();
            using (SqlCommand cmd = new SqlCommand())
            {
                cmd.Connection = conn;
                cmd.CommandType = CommandType.Text;
                cmd.CommandText = String.Format("SELECT @id = [schema_id] FROM {0}.sys.schemas WHERE [name] = '{1}';", DatabaseName, SchemaName);
                cmd.Parameters.Add("@id", SqlDbType.Int).Direction = ParameterDirection.Output;
                cmd.ExecuteNonQuery();
                return (int)cmd.Parameters[0].Value;
            }
        }
    }
}