All of the following images open in a new window for a detailed study. All of them are details taken from paintings.
Undershirts, or shifts, or in French chemises still seem not to have drawstrings, but to say they never have drawstrings would be wrong. One painting of Nell Gwynne by all means shows a drawstring in a casing, but all others show indeed a slit in the front or none at all and gathering into a band.
Shifts are generally made from a very fine linen, and when you want to recreate one, try to find the finest linen possible, because fine cotton batiste has a different feel and look to it than linen. If it is impossible to find a very fine linen, which is sadly often the case, then substitute with the aforementioned cotton batiste, which is softer than linen is and not cool to the touch. In some instances it will be necessary to substitute, for example the very sheer neckerchiefs, which just don't fall nor look right with available thin linens and in the later part of the Baroque period, the fine line caps, lappets for the fontange etc. Some looks cannot be achieved either regarding frills of cuffs, because the linen in modern thin weights cannot be gathered in such bulk and still fall so freely and luxuriously, but it appears to be too stiff and too thick. These are the times when you have to look for a good source of fine cotton batiste. In fact, cotton did start to replace the finest linen fabric, which is cambric, towards the end of the 17th century, but by the 1660s it was still linen which was the favourite, and of course the cheaper fabric.
One word, which is a very frustrating one, it is impossible to get such a fine linen cambric nowadays, and even when vendors try to sell you the so-called handkerchief linen for exorbitant prices, be aware it is not the fine sheer linen muslin in which the court beauties were so translucently and voluminously wrapped, because the flax plant that produced this extraordinarily fine linen thread died out in the 19th century due to climate changes. This is the same reason why even if there were still such skills around to produce this stunning Venetian Gros Point needlepoint lace, it is impossible, because the thread cannot be produced anymore. The plant is extinct.

It is very advisable not to save when it comes to the correct fabrics, all the work will be in vain and a magnificent silk upper class gown will look cheap if the fabrics are wrong, and this starts with the undergarments. Furthermore you need the shifts to soak up any perspiration and linen is the best in this, keeping you fairly cool in summer, cotton is the second best choice but it feels warmer. My own bodice, the blue one, shows large stains of perspiration on the linen lining, but the linen shift has worked a treat and even in the heat of the day at Vaux-le-Vicomte no stain appeared on the surface.

The chemise frills are double tired and very finely pleated. Lace edges the cuff frills and the sleeves are very wide.	The Duchess of Lauderdale wears a chemise that shows how the width of the fabric of the body is gathered at the neckline into a band.
Barbara Villiers Duchess of Cleveland's chemise shows the same gathering at the neckline and the same narrow band.	Nell Gwynne in an interesting chemise with a wide flounce and a slit in the front. The fullness appears to be gathered again onto a narrow band and the flounce is sewn onto it or the band sewn into the fine gathers. The narrow band would be used to tie the chemise closed at the slit.
The sleeves have double tiered cuff frills and are gathered with the help of interesting silk ribbons tied in wide and large bows.	Queen Henrietta Maria's chemise has sleeves with double lace tiers.
Nell Gwynne in the very famous portrait by Verelst and a chemise which shows that drawstrings were occasionally used. Here very clearly the extremely wide neckline was turned over at the top and in this fold a tunnel was created through which a ribbon was pulled. The ribbon can be seen in the front and the way the drawstring has creased the fold shows that indeed it is a drawstring. There is no way though with the linens available that this effect could be created, it would be far too thick and bulky in the neckline.	Drawing of a woman in a chemise which has fallen off her shoulders.