This can be done with a value converter hooked up to the Visibility property of the button in your template.

Below is some sample code showing how to create a simple value converter and how to hook it up to the Button in the template.

<UserControl x:Class="SilverlightApplication16.MainPage"

    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"

    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"

                   xmlns:local="clr-namespace:SilverlightApplication16"

                   xmlns:iggrid="clr-namespace:Infragistics.Silverlight.Controls;assembly=Infragistics.Silverlight.XamWebGrid.v9.2"

    xmlns:d="http://schemas.microsoft.com/expression/blend/2008" xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"

    mc:Ignorable="d" d:DesignWidth="640" d:DesignHeight="480">

  <Grid x:Name="LayoutRoot">

            <Grid.Resources>

                  <local:MyValueConverter x:Key="myConvert"></local:MyValueConverter>

            </Grid.Resources>

                  <iggrid:XamWebGrid x:Name="grid">

                  <iggrid:XamWebGrid.AddNewRowSettings>

                        <iggrid:AddNewRowSettings AllowAddNewRow="Top"></iggrid:AddNewRowSettings>

                  </iggrid:XamWebGrid.AddNewRowSettings>

                  <iggrid:XamWebGrid.Columns>

                        <iggrid:TemplateColumn Key="blah">

                              <iggrid:TemplateColumn.ItemTemplate>

                                    <DataTemplate>

                                          <Button Content="Delete"  Visibility="{Binding Converter={StaticResource myConvert}}" ></Button>

                                    </DataTemplate>

                              </iggrid:TemplateColumn.ItemTemplate>

                        </iggrid:TemplateColumn>

                  </iggrid:XamWebGrid.Columns>

            </iggrid:XamWebGrid>

      </Grid>

</UserControl>

public class MyValueConverter : IValueConverter

      {

            #region IValueConverter Members

            public object Convert(object value, Type targetType, object parameter, System.Globalization.CultureInfo culture)

            {

                  Person p = value as Person;

                  if (p == null || p.Name == null)

                  {

                        return Visibility.Collapsed;

                  }

                  return Visibility.Visible;

            }

            public object ConvertBack(object value, Type targetType, object parameter, System.Globalization.CultureInfo culture)

            {

                  throw new NotImplementedException();

            }

            #endregion

      }