こうですか？わかりません＞＜

FunctionKeyPressComponent.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.ComponentModel;
using System.Windows.Forms;

namespace WindowsFormsApplication1
{
    class FunctionKeyPressComponent : Component
    {
        private Form target;

        public Form Target
        {
            get { return target; }
            set {
                target = value;
                if (target == null) return;
                target.KeyDown += (s, e) =>
                    {
                        if (Keys.F1 <= e.KeyCode && e.KeyCode <= Keys.F12)
                        {
                            target.Text = e.KeyCode.ToString() + " Pressed!";
                            
                            // ファンクションキーの基底の動作を握り潰す
                            e.Handled = true;
                        }
                    };
            }
        }

    }
}

こうだと思います。

public partial class OmmitFunctionKeyDefaultActions : Component
{
    public OmmitFunctionKeyDefaultActions()
    {
        InitializeComponent();
        Disposed += OnDisposed;
    }

    public OmmitFunctionKeyDefaultActions(IContainer container)
    {
        container.Add(this);
        InitializeComponent();
        Disposed += OnDisposed;
    }

    private Form _targetForm;
    public Form TargetForm
    {
        get { return _targetForm; }
        set
        {
            if( _targetForm==value ) return;
            if (_targetForm != null)
            {
                _targetForm.KeyDown -= OnKeyDown;
            }
            _targetForm = value;
            if (_targetForm != null)
            {
                _targetForm.KeyDown += OnKeyDown;
            }
        }
    }

    private void OnDisposed(object sender, EventArgs e)
    {
        TargetForm = null;
    }

    private void OnKeyDown(object sender, KeyEventArgs e)
    {
        if (Keys.F1 <= e.KeyCode && e.KeyCode <= Keys.F12)
        {
            // ファンクションキーの基底の動作を握り潰す
            e.Handled = true;            
        }
    }
}